%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "1.29",
%%% date = "26 February 2020",
%%% time = "07:40:05 MST",
%%% filename = "toct.bib",
%%% address = "University of Utah
%%% Department of Mathematics, 110 LCB
%%% 155 S 1400 E RM 233
%%% Salt Lake City, UT 84112-0090
%%% USA",
%%% telephone = "+1 801 581 5254",
%%% FAX = "+1 801 581 4148",
%%% URL = "http://www.math.utah.edu/~beebe",
%%% checksum = "15286 7982 47194 417274",
%%% email = "beebe at math.utah.edu, beebe at acm.org,
%%% beebe at computer.org (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "bibliography, BibTeX, ACM Transactions on
%%% Computation Theory",
%%% license = "public domain",
%%% supported = "no",
%%% docstring = "This is a COMPLETE BibTeX bibliography for
%%% the journal ACM Transactions on Computation
%%% Theory (CODEN ????, ISSN 1942-3454),
%%% covering all journal issues from 2009 --
%%% date.
%%%
%%% The journal has a World-Wide Web site at:
%%%
%%% http://www.acm.org/pubs/toct
%%%
%%% Tables-of-contents are available at:
%%%
%%% http://www.acm.org/pubs/contents/journals/toct/
%%% http://portal.acm.org/browse_dl.cfm?idx=J1190
%%%
%%% Qualified subscribers can retrieve the full
%%% text of recent articles in PDF form.
%%%
%%% At version 1.29, the COMPLETE journal
%%% coverage looked like this:
%%%
%%% 2009 ( 7) 2013 ( 18) 2017 ( 10)
%%% 2010 ( 5) 2014 ( 21) 2018 ( 24)
%%% 2011 ( 6) 2015 ( 13) 2019 ( 28)
%%% 2012 ( 15) 2016 ( 23) 2020 ( 8)
%%%
%%% Article: 178
%%%
%%% Total entries: 178
%%%
%%% The initial draft was extracted from the
%%% ACM Web site, with manual corrections and
%%% additions from bibliographies in the TeX
%%% User Group collection, the author's
%%% personal bibliography files, the Compendex
%%% database, and a very large computer science
%%% bibliography collection on ftp.ira.uka.de
%%% in /pub/bibliography to which many people
%%% of have contributed. Where multiple
%%% sources of a particular entry existed,
%%% field values have been manually merged to
%%% preserve maximal information. Missing
%%% entries were identified by software
%%% developed for the TeX User Group and BibNet
%%% bibliography archive projects, and were
%%% then supplied from the original journal
%%% issues. Questions arising from conflicting
%%% data were resolved by consulting the
%%% original journal issues.
%%%
%%% ACM copyrights explicitly permit abstracting
%%% with credit, so article abstracts, keywords,
%%% and subject classifications have been
%%% included in this bibliography wherever
%%% available. Article reviews have been
%%% omitted, until their copyright status has
%%% been clarified.
%%%
%%% The bibsource keys in the bibliography
%%% entries below indicate the data sources,
%%% usually the Karlsruhe computer science
%%% bibliography archive for the first two
%%% volumes, or the journal Web site or the
%%% Compendex database, both of which lack
%%% coverage of this journal before 1985.
%%%
%%% URL keys in the bibliography point to
%%% World Wide Web locations of additional
%%% information about the entry.
%%%
%%% Spelling has been verified with the UNIX
%%% spell and GNU ispell programs using the
%%% exception dictionary stored in the
%%% companion file with extension .sok.
%%%
%%% BibTeX citation tags are uniformly chosen
%%% as name:year:abbrev, where name is the
%%% family name of the first author or editor,
%%% year is a 4-digit number, and abbrev is a
%%% 3-letter condensation of important title
%%% words. Citation tags were automatically
%%% generated by software developed for the
%%% BibNet Project.
%%%
%%% In this bibliography, entries are sorted in
%%% publication order, using ``bibsort -byvolume.''
%%%
%%% The checksum field above contains a CRC-16
%%% checksum as the first value, followed by the
%%% equivalent of the standard UNIX wc (word
%%% count) utility output of lines, words, and
%%% characters. This is produced by Robert
%%% Solovay's checksum utility.",
%%% }
%%% ====================================================================
@Preamble{"\input bibnames.sty"}
%%% ====================================================================
%%% Acknowledgement abbreviations:
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|http://www.math.utah.edu/~beebe/|"}
%%% ====================================================================
%%% Journal abbreviations:
@String{j-TOCT = "ACM Transactions on Computation Theory"}
%%% ====================================================================
%%% Publisher abbreviations:
@String{pub-ACM = "ACM Press"}
@String{pub-ACM:adr = "New York, NY 10036, USA"}
%%% ====================================================================
%%% Bibliography entries:
@Article{Fortnow:2009:EF,
author = "Lance Fortnow",
title = "{Editor}'s Foreword",
journal = j-TOCT,
volume = "1",
number = "1",
pages = "1:1--1:??",
month = feb,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1145/1490270.1490271",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Fri Apr 24 19:03:42 MDT 2009",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "1",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Aaronson:2009:ANB,
author = "Scott Aaronson and Avi Wigderson",
title = "Algebrization: a New Barrier in Complexity Theory",
journal = j-TOCT,
volume = "1",
number = "1",
pages = "2:1--2:??",
month = feb,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1145/1490270.1490272",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Fri Apr 24 19:03:42 MDT 2009",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Any proof of P $\neq$ NP will have to overcome two
barriers: {\em relativization\/} and {\em natural
proofs}. Yet over the last decade, we have seen circuit
lower bounds (e.g., that PP does not have linear-size
circuits) that overcome both barriers simultaneously.
So the question arises of whether there is a third
barrier to progress on the central questions in
complexity theory.\par
In this article, we present such a barrier, which we
call {\em algebraic relativization\/} or {\em
algebrization}. The idea is that, when we relativize
some complexity class inclusion, we should give the
simulating machine access not only to an oracle $A$,
but also to a low-degree extension of $A$ over a finite
field or ring.\par
We systematically go through basic results and open
problems in complexity theory to delineate the power of
the new algebrization barrier. First, we show that all
known nonrelativizing results based on
arithmetization---both inclusions such as IP = PSPACE
and MIP = NEXP, and separations such as MA$_{{EXP}_n}$
P/poly---do indeed algebrize. Second, we show that
almost all of the major open problems---including P
versus NP, P versus RP, and NEXP versus P/poly---will
require {\em non-algebrizing techniques}. In some
cases, algebrization seems to explain exactly why
progress stopped where it did: for example, why we have
superlinear circuit lower bounds for PromiseMA but not
for NP.\par
Our second set of results follows from lower bounds in
a new model of {\em algebraic query complexity}, which
we introduce in this article and which is interesting
in its own right. Some of our lower bounds use direct
combinatorial and algebraic arguments, while others
stem from a surprising connection between our model and
communication complexity. Using this connection, we are
also able to give an MA-protocol for the Inner Product
function with $O(\sqrt{n} \log n)$ communication
(essentially matching a lower bound of Klauck), as well
as a communication complexity conjecture whose truth
would imply NL $\neq$ NP.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
keywords = "arithmetization; communication complexity; interactive
proofs; Low-degree polynomials; oracles; query
complexity",
}
@Article{Razborov:2009:SPB,
author = "Alexander Razborov",
title = "A Simple Proof of {Bazzi's Theorem}",
journal = j-TOCT,
volume = "1",
number = "1",
pages = "3:1--3:??",
month = feb,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1145/1490270.1490273",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Fri Apr 24 19:03:42 MDT 2009",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Linial and Nisan [1990] asked if any polylog-wise
independent distribution fools any function in AC$^0$.
In a recent remarkable development, Bazzi solved this
problem for the case of DNF formulas. The aim of this
note is to present a simplified version of his proof.",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
keywords = "DNF; Pseudo-random generators",
}
@Article{Bourke:2009:DPR,
author = "Chris Bourke and Raghunath Tewari and N. V.
Vinodchandran",
title = "Directed Planar Reachability Is in Unambiguous
Log-Space",
journal = j-TOCT,
volume = "1",
number = "1",
pages = "4:1--4:??",
month = feb,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1145/1490270.1490274",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Fri Apr 24 19:03:42 MDT 2009",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We make progress in understanding the complexity of
the graph reachability problem in the context of
unambiguous logarithmic space computation; a restricted
form of nondeterminism. As our main result, we show a
new upper bound on the {\em directed planar
reachability problem\/} by showing that it can be
decided in the class unambiguous logarithmic space
(UL). We explore the possibility of showing the same
upper bound for the general graph reachability problem.
We give a simple reduction showing that the
reachability problem for directed graphs with thickness
two is complete for the class nondeterministic
logarithmic space (NL). Hence an extension of our
results to directed graphs with thickness two will
unconditionally collapse NL to UL.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
keywords = "Directed graph reachability; planar graphs;
unambiguous log-space",
}
@Article{David:2009:ISB,
author = "Matei David and Toniann Pitassi and Emanuele Viola",
title = "Improved Separations between Nondeterministic and
Randomized Multiparty Communication",
journal = j-TOCT,
volume = "1",
number = "2",
pages = "5:1--5:??",
month = sep,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1145/1595391.1595392",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Tue Mar 16 10:08:03 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Guruswami:2009:HSS,
author = "Venkatesan Guruswami and Prasad Raghavendra",
title = "Hardness of Solving Sparse Overdetermined Linear
Systems: a 3-Query {PCP} over Integers",
journal = j-TOCT,
volume = "1",
number = "2",
pages = "6:1--6:??",
month = sep,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1145/1595391.1595393",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Tue Mar 16 10:08:03 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Ben-Sasson:2009:SQP,
author = "Eli Ben-Sasson and Prahladh Harsha and Oded Lachish
and Arie Matsliah",
title = "Sound 3-Query {PCPPs} Are Long",
journal = j-TOCT,
volume = "1",
number = "2",
pages = "7:1--7:??",
month = sep,
year = "2009",
CODEN = "????",
DOI = "https://doi.org/10.1145/1595391.1595394",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Tue Mar 16 10:08:03 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Kyncl:2010:LRD,
author = "Jan Kyn{\v{c}}l and Tom{\'a}{\v{s}} Vysko{\v{c}}il",
title = "Logspace Reduction of Directed Reachability for
Bounded Genus Graphs to the Planar Case",
journal = j-TOCT,
volume = "1",
number = "3",
pages = "8:1--8:??",
month = mar,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1145/1714450.1714451",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Tue Mar 16 10:08:04 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Beame:2010:FCD,
author = "Paul Beame and Russell Impagliazzo and Toniann Pitassi
and Nathan Segerlind",
title = "Formula Caching in {DPLL}",
journal = j-TOCT,
volume = "1",
number = "3",
pages = "9:1--9:??",
month = mar,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1145/1714450.1714452",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Tue Mar 16 10:08:04 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Datta:2010:PDP,
author = "Samir Datta and Raghav Kulkarni and Nutan Limaye and
Meena Mahajan",
title = "Planarity, Determinants, Permanents, and (Unique)
Matchings",
journal = j-TOCT,
volume = "1",
number = "3",
pages = "10:1--10:??",
month = mar,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1145/1714450.1714453",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Tue Mar 16 10:08:04 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "10",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Yin:2010:CPP,
author = "Yitong Yin",
title = "Cell-Probe Proofs",
journal = j-TOCT,
volume = "2",
number = "1",
pages = "1:1--1:??",
month = nov,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1145/1867719.1867720",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Tue Nov 23 11:20:48 MST 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "1",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Hoefer:2010:TAC,
author = "Martin Hoefer and Alexander Souza",
title = "Tradeoffs and Average-Case Equilibria in Selfish
Routing",
journal = j-TOCT,
volume = "2",
number = "1",
pages = "2:1--2:??",
month = nov,
year = "2010",
CODEN = "????",
DOI = "https://doi.org/10.1145/1867719.1867721",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Tue Nov 23 11:20:48 MST 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Purdy:2011:LBC,
author = "Eric Purdy",
title = "Lower Bounds for Coin-Weighing Problems",
journal = j-TOCT,
volume = "2",
number = "2",
pages = "3:1--3:??",
month = mar,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1145/1944857.1944858",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Mon Mar 28 09:50:20 MDT 2011",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Arvind:2011:SGI,
author = "Vikraman Arvind and Jacobo Tor{\'a}n",
title = "Solvable Group Isomorphism Is (Almost) in {NP} $\cap$
{coNP}",
journal = j-TOCT,
volume = "2",
number = "2",
pages = "4:1--4:??",
month = mar,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1145/1944857.1944859",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Mon Mar 28 09:50:20 MDT 2011",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Fellows:2011:CDF,
author = "Michael R. Fellows and Jiong Guo and Hannes Moser and
Rolf Niedermeier",
title = "A Complexity Dichotomy for Finding Disjoint Solutions
of Vertex Deletion Problems",
journal = j-TOCT,
volume = "2",
number = "2",
pages = "5:1--5:??",
month = mar,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1145/1944857.1944860",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Mon Mar 28 09:50:20 MDT 2011",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Hitchcock:2011:KCR,
author = "John M. Hitchcock and A. Pavan and N. V.
Vinodchandran",
title = "{Kolmogorov} Complexity in Randomness Extraction",
journal = j-TOCT,
volume = "3",
number = "1",
pages = "1:1--1:??",
month = aug,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1145/2003685.2003686",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Mon Sep 5 16:58:07 MDT 2011",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "1",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Kulkarni:2011:PIP,
author = "Raghav Kulkarni",
title = "On the Power of Isolation in Planar Graphs",
journal = j-TOCT,
volume = "3",
number = "1",
pages = "2:1--2:??",
month = aug,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1145/2003685.2003687",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Mon Sep 5 16:58:07 MDT 2011",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Smyth:2011:AQC,
author = "Clifford Smyth",
title = "Approximate Query Complexity",
journal = j-TOCT,
volume = "3",
number = "1",
pages = "3:1--3:??",
month = aug,
year = "2011",
CODEN = "????",
DOI = "https://doi.org/10.1145/2003685.2003688",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
bibdate = "Mon Sep 5 16:58:07 MDT 2011",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Cook:2012:PBP,
author = "Stephen Cook and Pierre McKenzie and Dustin Wehr and
Mark Braverman and Rahul Santhanam",
title = "Pebbles and Branching Programs for Tree Evaluation",
journal = j-TOCT,
volume = "3",
number = "2",
pages = "4:1--4:??",
month = jan,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2077336.2077337",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Fri Mar 16 15:22:48 MDT 2012",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We introduce the tree evaluation problem, show that it
is in LogDCFL (and hence in $P$), and study its
branching program complexity in the hope of eventually
proving a superlogarithmic space lower bound. The input
to the problem is a rooted, balanced $d$-ary tree of
height h, whose internal nodes are labeled with $d$-ary
functions on $[ k ] = {1,\ldots{}, k}$, and whose
leaves are labeled with elements of $[ k ]$. Each node
obtains a value in $[ k ]$ equal to its $d$-ary
function applied to the values of its $d$ children. The
output is the value of the root. We show that the
standard black pebbling algorithm applied to the binary
tree of height h yields a deterministic $k$-way
branching program with $O(k h)$ states solving this
problem, and we prove that this upper bound is tight
for $h = 2$ and $h = 3$. We introduce a simple semantic
restriction called thrifty on $k$-way branching
programs solving tree evaluation problems and show that
the same state bound of $\Theta ( k h)$ is tight for
all $h \geq 2$ for deterministic thrifty programs. We
introduce fractional pebbling for trees and show that
this yields nondeterministic thrifty programs with
$\Theta(k h/2 + 1)$ states solving the Boolean problem
`determine whether the root has value 1', and prove
that this bound is tight for $h = 2, 3, 4$. We also
prove that this same bound is tight for unrestricted
nondeterministic $k$-way branching programs solving the
Boolean problem for $h = 2, 3$.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Gal:2012:TQL,
author = "Anna Gal and Andrew Mills",
title = "Three-Query Locally Decodable Codes with Higher
Correctness Require Exponential Length",
journal = j-TOCT,
volume = "3",
number = "2",
pages = "5:1--5:??",
month = jan,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2077336.2077338",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Fri Mar 16 15:22:48 MDT 2012",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Locally decodable codes are error-correcting codes
with the extra property that, in order to retrieve the
value of a single input position, it is sufficient to
read a small number of positions of the codeword. We
refer to the probability of getting the correct value
as the correctness of the decoding algorithm. A
breakthrough result by Yekhanin [2007] showed that
3-query linear locally decodable codes may have
subexponential length. The construction of Yekhanin,
and the three query constructions that followed,
achieve correctness only up to a certain limit which is
1--3 $\delta$ for nonbinary codes, where an adversary
is allowed to corrupt up to $\delta$ fraction of the
codeword. The largest correctness for a subexponential
length 3-query binary code is achieved in a
construction by Woodruff [2008], and it is below 1--3
$\delta$. We show that achieving slightly larger
correctness (as a function of $\delta$) requires
exponential codeword length for 3-query codes.
Previously, there were no larger than quadratic lower
bounds known for locally decodable codes with more than
2 queries, even in the case of 3-query linear codes.
Our lower bounds hold for linear codes over arbitrary
finite fields and for binary nonlinear codes.
Considering larger number of queries, we obtain lower
bounds for $q$-query codes for $q > 3$, under certain
assumptions on the decoding algorithm that have been
commonly used in previous constructions. We also prove
bounds on the largest correctness achievable by these
decoding algorithms, regardless of the length of the
code. Our results explain the limitations on
correctness in previous constructions using such
decoding algorithms. In addition, our results imply
trade-offs on the parameters of error-correcting data
structures.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Beame:2012:VMR,
author = "Paul Beame and Trinh Huynh",
title = "The Value of Multiple {Read\slash} Write Streams for
Approximating Frequency Moments",
journal = j-TOCT,
volume = "3",
number = "2",
pages = "6:1--6:??",
month = jan,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2077336.2077339",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Fri Mar 16 15:22:48 MDT 2012",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We consider the read/write streams model, an extension
of the standard data stream model in which an algorithm
can create and manipulate multiple read/write streams
in addition to its input data stream. Like the data
stream model, the most important parameter for this
model is the amount of internal memory used by such an
algorithm. The other key parameters are the number of
streams the algorithm uses and the number of passes it
makes on these streams. We consider how the addition of
multiple streams impacts the ability of algorithms to
approximate the frequency moments of the input stream.
We show that any randomized read/write stream algorithm
with a fixed number of streams and a sublogarithmic
number of passes that produces a constant factor
approximation of the $k$ -th frequency moment $F_k$ of
an input sequence of length of at most $N$ from
$\{1,\ldots{},N\}$ requires space $\Omega(N^{1 - 4/k -
\delta})$ for any $\delta > 0$. For comparison, it is
known that with a single read-only one-pass data stream
there is a randomized constant-factor approximation for
$F_k$ using $\tilde{O}(N^{1 - 2/k})$ space, and that by
sorting, which can be done deterministically in $O(\log
N)$ passes using $3$ read/write streams, $F_k$ can be
computed exactly. Therefore, although the ability to
manipulate multiple read/write streams can add
substantial power to the data stream model, with a
sublogarithmic number of passes this does not
significantly improve the ability to approximate higher
frequency moments efficiently. We obtain our results by
showing a new connection between the read/write streams
model and the multiparty number-in-hand communication
model.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Tani:2012:EQA,
author = "Seiichiro Tani and Hirotada Kobayashi and Keiji
Matsumoto",
title = "Exact Quantum Algorithms for the Leader Election
Problem",
journal = j-TOCT,
volume = "4",
number = "1",
pages = "1:1--1:??",
month = mar,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2141938.2141939",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Nov 6 18:23:48 MST 2012",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "This article gives a separation between quantum and
classical models in pure (i.e., noncryptographic)
computing abilities with no restriction on the amount
of available computing resources, by considering the
exact solvability of the leader election problem in
anonymous networks, a celebrated unsolvable problem in
classical distributed computing. The goal of the leader
election problem is to elect a unique leader from among
distributed parties. In an anonymous network, all
parties with the same number of communication links are
identical. It is well-known that no classical algorithm
can exactly solve (i.e., in bounded time without error)
the leader election problem in anonymous networks, even
if the number of parties is given. This article devises
a quantum algorithm that, if the number of parties is
given, exactly solves the problem for any network
topology in polynomial rounds with polynomial
communication/time complexity with respect to the
number of parties, when the parties are connected with
quantum communication links and they have the ability
of quantum computing. Our algorithm works even when
only an upper bound of the number of parties is given.
In such a case, no classical algorithm can solve the
problem even under the zero-error setting, the setting
in which error is not allowed but running time may be
unbounded.",
acknowledgement = ack-nhfb,
articleno = "1",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Cheraghchi:2012:ALT,
author = "Mahdi Cheraghchi and Johan H{\aa}stad and Marcus
Isaksson and Ola Svensson",
title = "Approximating Linear Threshold Predicates",
journal = j-TOCT,
volume = "4",
number = "1",
pages = "2:1--2:??",
month = mar,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2141938.2141940",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Nov 6 18:23:48 MST 2012",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We study constraint satisfaction problems on the
domain {-1, 1}, where the given constraints are
homogeneous linear threshold predicates, that is,
predicates of the form $\sgn(w_1 x_1 + \cdots + w_n
x_n)$ for some positive integer weights $w_1, \ldots{},
w_n$. Despite their simplicity, current techniques fall
short of providing a classification of these predicates
in terms of approximability. In fact, it is not easy to
guess whether there exists a homogeneous linear
threshold predicate that is approximation resistant or
not. The focus of this article is to identify and study
the approximation curve of a class of threshold
predicates that allow for nontrivial
approximation. Arguably the simplest such predicate is
the majority predicate $\sgn(x_1 + \cdots + x_n)$, for
which we obtain an almost complete understanding of the
asymptotic approximation curve, assuming the Unique
Games Conjecture. Our techniques extend to a more
general class of ``majority-like'' predicates and we
obtain parallel results for them. In order to classify
these predicates, we introduce the notion of
Chow-robustness that might be of independent
interest.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{De:2012:ELB,
author = "Anindya De and Thomas Watson",
title = "Extractors and Lower Bounds for Locally Samplable
Sources",
journal = j-TOCT,
volume = "4",
number = "1",
pages = "3:1--3:??",
month = mar,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2141938.2141941",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Nov 6 18:23:48 MST 2012",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We consider the problem of extracting randomness from
sources that are efficiently samplable, in the sense
that each output bit of the sampler only depends on
some small number $d$ of the random input bits. As our
main result, we construct a deterministic extractor
that, given any $d$-local source with min-entropy $k$
on $n$ bits, extracts $\Omega(k^2 / n d)$ bits that are
$2^{-n \Omega (1)}$-close to uniform, provided $d \leq
o(\log n)$ and $k \geq n^{2/3 + \gamma}$ (for
arbitrarily small constants $\gamma > 0$). Using our
result, we also improve a result of Viola [2010] who
proved a $1/2 O(1/\log n)$ statistical distance lower
bound for $o(\log n)$-local samplers trying to sample
input-output pairs of an explicit boolean function,
assuming the samplers use at most $n + n^{1 - \delta}$
random bits for some constant $\delta > 0$. Using a
different function, we simultaneously improve the lower
bound to $1/2 - 2^{-n \Omega (1)}$ and eliminate the
restriction on the number of random bits.",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Schoenebeck:2012:CCN,
author = "Grant R. Schoenebeck and Salil Vadhan",
title = "The Computational Complexity of {Nash} Equilibria in
Concisely Represented Games",
journal = j-TOCT,
volume = "4",
number = "2",
pages = "4:1--4:??",
month = may,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2189778.2189779",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Nov 6 18:23:49 MST 2012",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Games may be represented in many different ways, and
different representations of games affect the
complexity of problems associated with games, such as
finding a Nash equilibrium. The traditional method of
representing a game is to explicitly list all the
payoffs, but this incurs an exponential blowup as the
number of agents grows. We study two models of
concisely represented games: circuit games, where the
payoffs are computed by a given boolean circuit, and
graph games, where each agent's payoff is a function of
only the strategies played by its neighbors in a given
graph. For these two models, we study the complexity of
four questions: determining if a given strategy is a
Nash equilibrium, finding a Nash equilibrium,
determining if there exists a pure Nash equilibrium,
and determining if there exists a Nash equilibrium in
which the payoffs to a player meet some given
guarantees. In many cases, we obtain tight results,
showing that the problems are complete for various
complexity classes.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Kawamura:2012:CTO,
author = "Akitoshi Kawamura and Stephen Cook",
title = "Complexity Theory for Operators in Analysis",
journal = j-TOCT,
volume = "4",
number = "2",
pages = "5:1--5:??",
month = may,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2189778.2189780",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Nov 6 18:23:49 MST 2012",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We propose an extension of the framework for
discussing the computational complexity of problems
involving uncountably many objects, such as real
numbers, sets and functions, that can be represented
only through approximation. The key idea is to use a
certain class of string functions as names representing
these objects. These are more expressive than infinite
sequences, which served as names in prior work that
formulated complexity in more restricted settings. An
advantage of using string functions is that we can
define their size in a way inspired by higher-type
complexity theory. This enables us to talk about
computation on string functions whose time or space is
bounded polynomially in the input size, giving rise to
more general analogues of the classes P, NP, and
PSPACE. We also define NP- and PSPACE-completeness
under suitable many-one reductions. Because our
framework separates machine computation and semantics,
it can be applied to problems on sets of interest in
analysis once we specify a suitable representation
(encoding). As prototype applications, we consider the
complexity of functions (operators) on real numbers,
real sets, and real functions. For example, the task of
numerical algorithms for solving a certain class of
differential equations is naturally viewed as an
operator taking real functions to real functions. As
there was no complexity theory for operators, previous
results only stated how complex the solution can be. We
now reformulate them and show that the operator itself
is polynomial-space complete.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Penna:2012:CRM,
author = "Paolo Penna and Carmine Ventre",
title = "Collusion-Resistant Mechanisms with Verification
Yielding Optimal Solutions",
journal = j-TOCT,
volume = "4",
number = "2",
pages = "6:1--6:??",
month = may,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2189778.2189781",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Nov 6 18:23:49 MST 2012",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "A truthful mechanism consists of an algorithm
augmented with a suitable payment function that
guarantees that the players cannot improve their
utilities by cheating. Mechanism design approaches are
particularly appealing for designing protocols that
cannot be manipulated by rational players. We present
new constructions of so-called mechanisms with
verification introduced by Nisan and Ronen [2001]. We
first show how to obtain mechanisms that, for
single-parameter domains, are resistant to coalitions
of colluding agents even if they can exchange
compensations. Based on this result we derive a class
of exact truthful mechanisms with verification for
arbitrary bounded domains. This class of problems
includes most of the problems studied in the
algorithmic mechanism design literature and for which
exact solutions cannot be obtained with truthful
mechanisms without verification. This result is an
improvement over all known previous constructions of
exact mechanisms with verification.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Beyersdorff:2012:PBD,
author = "Olaf Beyersdorff and Nicola Galesi and Massimo Lauria
and Alexander A. Razborov",
title = "Parameterized Bounded-Depth {Frege} Is not Optimal",
journal = j-TOCT,
volume = "4",
number = "3",
pages = "7:1--7:??",
month = sep,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2355580.2355582",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Nov 6 18:23:50 MST 2012",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "A general framework for parameterized proof complexity
was introduced by Dantchev et al. [2007]. There, the
authors show important results on tree-like
Parameterized Resolution---a parameterized version of
classical Resolution---and their gap complexity theorem
implies lower bounds for that system. The main result
of this article significantly improves upon this by
showing optimal lower bounds for a parameterized
version of bounded-depth Frege. More precisely, we
prove that the pigeonhole principle requires proofs of
size n$^{\Omega (k)}$ in parameterized bounded-depth
Frege, and, as a special case, in dag-like
Parameterized Resolution. This answers an open question
posed in Dantchev et al. [2007]. In the opposite
direction, we interpret a well-known technique for FPT
algorithms as a DPLL procedure for Parameterized
Resolution. Its generalization leads to a proof search
algorithm for Parameterized Resolution that in
particular shows that tree-like Parameterized
Resolution allows short refutations of all
parameterized contradictions given as bounded-width
CNFs.",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Watson:2012:RWW,
author = "Thomas Watson",
title = "Relativized Worlds without Worst-Case to Average-Case
Reductions for {NP}",
journal = j-TOCT,
volume = "4",
number = "3",
pages = "8:1--8:??",
month = sep,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2355580.2355583",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Nov 6 18:23:50 MST 2012",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We prove that, relative to an oracle, there is no
worst-case to average-case reduction for NP. We also
handle classes that are somewhat larger than NP, as
well as worst-case to errorless -average-case
reductions. In fact, we prove that relative to an
oracle, there is no worst-case to
errorless-average-case reduction from NP to
BPP$_{||}^{NP}$. We also handle reductions from NP to
the polynomial-time hierarchy and beyond, under strong
restrictions on the number of queries the reductions
can make.",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Kayal:2012:SSR,
author = "Neeraj Kayal and Chandan Saha",
title = "On the Sum of Square Roots of Polynomials and Related
Problems",
journal = j-TOCT,
volume = "4",
number = "4",
pages = "9:1--9:??",
month = nov,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2382559.2382560",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Sun May 5 09:31:28 MDT 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The sum of square roots over integers problem is the
task of deciding the sign of a nonzero sum, {$ S =
\Sigma_{i = 1}^n \delta_i \cdot \sqrt a_i $}, where
\delta $_i$ \in {+1, -1} and a$_i$ 's are positive
integers that are upper bounded by {$N$} (say). A
fundamental open question in numerical analysis and
computational geometry is whether {$ | S | \geq 1 /
2^{(n \cdot \log N) O(1)} $} when {$ S \neq 0 $}. We
study a formulation of this problem over polynomials.
Given an expression {$ S = \Sigma_{i = 1}^n c_i \cdot
\sqrt f_i (x) $}, where $ c_i $'s belong to a field of
characteristic $0$ and $ f_i $'s are univariate
polynomials with degree bounded by $d$ and $ f_i(0)
\neq 0 $ for all $i$, is it true that the minimum
exponent of $x$ that has a nonzero coefficient in the
power series {$S$} is upper bounded by {$ (n \cdot
d)^{O(1)} $}, unless {$ S = 0 $}? We answer this
question affirmatively. Further, we show that this
result over polynomials can be used to settle
(positively) the sum of square roots problem for a
special class of integers: Suppose each integer $ a_i $
is of the form, {$ a_i = X^d_i + b_{i1} X^{di - 1} +
\ldots {} + b_{idi} $}, $ d_i > 0 $, where {$X$} is a
positive real number and $ b_{ij} $'s are integers. Let
{$ B = \max (| b_{ij} |_{i, j}, 1) $} and $ d = \max_i
\{ d_i \} $. If {$ X > (B + 1)^{(n \cdot d)O(1)} $}
then a nonzero {$ S = \Sigma_{i = 1}^n \delta_i \sqrt
a_i $} is lower bounded as {$ | S | \geq 1 / X^(n \cdot
d)O(1) $}. The constant in {$ O (1) $}, as fixed by our
analysis, is roughly $2$. We then consider the
following more general problem. Given an arithmetic
circuit computing a multivariate polynomial {$ f (X) $}
and integer $d$, is the degree of {$ f (X) $} less than
or equal to $d$ ? We give a {coRP$^{PP}$}-algorithm for
this problem, improving previous results of Allender et
al. [2009] and Koiran and Perifel [2007].",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Pass:2012:PRT,
author = "Rafael Pass and Muthuramakrishnan Venkitasubramaniam",
title = "A Parallel Repetition Theorem for Constant-Round
{Arthur--Merlin} Proofs",
journal = j-TOCT,
volume = "4",
number = "4",
pages = "10:1--10:??",
month = nov,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2382559.2382561",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Sun May 5 09:31:28 MDT 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We show a parallel-repetition theorem for
constant-round Arthur--Merlin Proofs, using an
efficient reduction. As a consequence, we show that
parallel repetition reduces the soundness-error at an
optimal rate (up to a negligible factor) in
constant-round public-coin argument systems, and
constant-round public-coin proofs of knowledge. The
first of these results resolves an open question posed
by Bellare, Impagliazzo, and Naor (FOCS'97).",
acknowledgement = ack-nhfb,
articleno = "10",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Ron:2012:AIM,
author = "Dana Ron and Ronitt Rubinfeld and Muli Safra and Alex
Samorodnitsky and Omri Weinstein",
title = "Approximating the Influence of Monotone {Boolean}
Functions in {$ O(\sqrt n) $} Query Complexity",
journal = j-TOCT,
volume = "4",
number = "4",
pages = "11:1--11:??",
month = nov,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2382559.2382562",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Sun May 5 09:31:28 MDT 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The Total Influence ( Average Sensitivity ) of a
discrete function is one of its fundamental measures.
We study the problem of approximating the total
influence of a monotone Boolean function, which we
denote by {$ I[f] $}. We present a randomized algorithm
that approximates the influence of such functions to
within a multiplicative factor of $ (1 \pm \epsilon) $
by performing {$ O(\sqrt n I[f] \poly (1 / \epsilon))
$} queries. We also prove a lower bound of {$ \Omega
(\sqrt n \log n \cdot I[f]) $} on the query complexity
of any constant factor approximation algorithm for this
problem (which holds for {$ I[f] = \Omega (1) $}),
hence showing that our algorithm is almost optimal in
terms of its dependence on $n$. For general functions,
we give a lower bound of {$ \Omega (n I[f]) $}, which
matches the complexity of a simple sampling
algorithm.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Vlassis:2012:CCS,
author = "Nikos Vlassis and Michael L. Littman and David
Barber",
title = "On the Computational Complexity of Stochastic
Controller Optimization in {POMDPs}",
journal = j-TOCT,
volume = "4",
number = "4",
pages = "12:1--12:??",
month = nov,
year = "2012",
CODEN = "????",
DOI = "https://doi.org/10.1145/2382559.2382563",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Sun May 5 09:31:28 MDT 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We show that the problem of finding an optimal
stochastic blind controller in a Markov decision
process is an NP-hard problem. The corresponding
decision problem is NP-hard in PSPACE and
sqrt-sum-hard, hence placing it in NP would imply
breakthroughs in long-standing open problems in
computer science. Our result establishes that the more
general problem of stochastic controller optimization
in POMDPs is also NP-hard. Nonetheless, we outline a
special case that is convex and admits efficient global
solutions.",
acknowledgement = ack-nhfb,
articleno = "12",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Austrin:2013:UP,
author = "Per Austrin and Johan H{\aa}stad",
title = "On the usefulness of predicates",
journal = j-TOCT,
volume = "5",
number = "1",
pages = "1:1--1:??",
month = may,
year = "2013",
CODEN = "????",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:04 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Motivated by the pervasiveness of strong
inapproximability results for Max-CSPs, we introduce a
relaxed notion of an approximate solution of a Max-CSP.
In this relaxed version, loosely speaking, the
algorithm is allowed to replace the constraints of an
instance by some other (possibly real-valued)
constraints, and then only needs to satisfy as many of
the new constraints as possible. To be more precise, we
introduce the following notion of a predicate $P$ being
useful for a (real-valued) objective $Q$: given an
almost satisfiable Max- $P$ instance, there is an
algorithm that beats a random assignment on the
corresponding Max-$Q$ instance applied to the same sets
of literals. The standard notion of a nontrivial
approximation algorithm for a Max-CSP with predicate
$P$ is exactly the same as saying that $P$ is useful
for $P$ itself. We say that $P$ is useless if it is not
useful for any $Q$. This turns out to be equivalent to
the following pseudo-randomness property: given an
almost satisfiable instance of Max- $P$, it is hard to
find an assignment such that the induced distribution
on k -bit strings defined by the instance is not
essentially uniform. Under the unique games conjecture,
we give a complete and simple characterization of
useful Max-CSPs defined by a predicate: such a Max-CSP
is useless if and only if there is a pairwise
independent distribution supported on the satisfying
assignments of the predicate. It is natural to also
consider the case when no negations are allowed in the
CSP instance, and we derive a similar complete
characterization (under the UGC) there as well.
Finally, we also include some results and examples
shedding additional light on the approximability of
certain Max-CSPs.",
acknowledgement = ack-nhfb,
articleno = "1",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Beyersdorff:2013:VPC,
author = "Olaf Beyersdorff and Samir Datta and Andreas Krebs and
Meena Mahajan and Gido Scharfenberger-Fabian and
Karteek Sreenivasaiah and Michael Thomas and Heribert
Vollmer",
title = "Verifying proofs in constant depth",
journal = j-TOCT,
volume = "5",
number = "1",
pages = "2:1--2:??",
month = may,
year = "2013",
CODEN = "????",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:04 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "In this paper we initiate the study of proof systems
where verification of proofs proceeds by NC$^0$
circuits. We investigate the question which languages
admit proof systems in this very restricted model.
Formulated alternatively, we ask which languages can be
enumerated by NC$^0$ functions. Our results show that
the answer to this problem is not determined by the
complexity of the language. On the one hand, we
construct NC$^0$ proof systems for a variety of
languages ranging from regular to NP complete. On the
other hand, we show by combinatorial methods that even
easy regular languages such as Exact-OR do not admit
NC$^0$ proof systems. We also show that Majority does
not admit NC$^0$ proof systems. Finally, we present a
general construction of NC$^0$ proof systems for
regular languages with strongly connected NFA's.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Cygan:2013:MCP,
author = "Marek Cygan and Marcin Pilipczuk and Michal Pilipczuk
and Jakub Onufry Wojtaszczyk",
title = "On multiway cut parameterized above lower bounds",
journal = j-TOCT,
volume = "5",
number = "1",
pages = "3:1--3:??",
month = may,
year = "2013",
CODEN = "????",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:04 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We introduce a concept of parameterizing a problem
above the optimum solution of its natural linear
programming relaxation and prove that the node multiway
cut problem is fixed-parameter tractable (FPT) in this
setting. As a consequence we prove that node multiway
cut is FPT, when parameterized above the maximum
separating cut, resolving an open problem of Razgon.
Our results imply $ O^*(4^k) $ algorithms for vertex
cover above maximum matching and almost 2-SAT as well
as an $ O^*(2^k) $ algorithm for node multiway cut with
a standard parameterization by the solution size,
improving previous bounds for these problems.",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Englert:2013:EC,
author = "Matthias Englert and Heiko R{\"o}glin and Jacob
Sp{\"o}nemann and Berthold V{\"o}cking",
title = "Economical Caching",
journal = j-TOCT,
volume = "5",
number = "2",
pages = "4:1--4:??",
month = jul,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2493246.2493247",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:08 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We study the management of buffers and storages in
environments with unpredictably varying prices in a
competitive analysis. In the economical caching
problem, there is a storage with a certain capacity.
For each time step, an online algorithm is given a
price from the interval $ [1, \alpha] $, a consumption,
and possibly a buying limit. The online algorithm has
to decide the amount to purchase from some commodity,
knowing the parameter $ \alpha $ but without knowing
how the price evolves in the future. The algorithm can
purchase at most the buying limit. If it purchases more
than the current consumption, then the excess is stored
in the storage; otherwise, the gap between consumption
and purchase must be taken from the storage. The goal
is to minimize the total cost. Interesting motivating
applications are, for example, stream caching on mobile
devices with different classes of service, battery
management in micro hybrid cars, and the efficient
purchase of resources. First we consider the simple but
natural class of algorithms that can informally be
described as memoryless. We show that these algorithms
cannot achieve a competitive ratio below $ \sqrt \alpha
$. Then we present a more sophisticated deterministic
algorithm achieving a competitive ratio of where $W$
denotes the Lambert $W$ function. We prove that this
algorithm is optimal and that not even randomized
online algorithms can achieve a better competitive
ratio. On the other hand, we show how to achieve a
constant competitive ratio if the storage capacity of
the online algorithm exceeds the storage capacity of an
optimal offline algorithm by a factor of $ \log \alpha
$.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Bogdanov:2013:HFL,
author = "Andrej Bogdanov and Akinori Kawachi and Hidetoki
Tanaka",
title = "Hard Functions for Low-Degree Polynomials over Prime
Fields",
journal = j-TOCT,
volume = "5",
number = "2",
pages = "5:1--5:??",
month = jul,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2493246.2493248",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:08 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "In this article, we present a new hardness
amplification for low-degree polynomials over prime
fields, namely, we prove that if some function is
mildly hard to approximate by any low-degree
polynomials then the sum of independent copies of the
function is very hard to approximate by them. This
result generalizes the XOR lemma for low-degree
polynomials over the binary field given by Viola and
Wigderson [2008]. The main technical contribution is
the analysis of the Gowers norm over prime fields. For
the analysis, we discuss a generalized low-degree test,
which we call the Gowers test, for polynomials over
prime fields, which is a natural generalization of that
over the binary field given by Alon et al. [2003]. This
Gowers test provides a new technique to analyze the
Gowers norm over prime fields. Actually, the rejection
probability of the Gowers test can be analyzed in the
framework of Kaufman and Sudan [2008]. However, our
analysis is self-contained and quantitatively better.
By using our argument, we also prove the hardness of
modulo functions for low-degree polynomials over prime
fields.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Williams:2013:ATP,
author = "Ryan Williams",
title = "Alternation-Trading Proofs, Linear Programming, and
Lower Bounds",
journal = j-TOCT,
volume = "5",
number = "2",
pages = "6:1--6:??",
month = jul,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2493246.2493249",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:08 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "A fertile area of recent research has demonstrated
concrete polynomial-time lower bounds for natural hard
problems on restricted computational models. Among
these problems are Satisfiability, Vertex Cover,
Hamilton Path, MOD$_6$-SAT, Majority-of-Majority-SAT,
and Tautologies, to name a few. The proofs of these
lower bounds follow a proof-by-contradiction strategy
that we call resource trading or alternation trading.
An important open problem is to determine how powerful
such proofs can possibly be. We propose a methodology
for studying these proofs that makes them amenable to
both formal analysis and automated theorem proving. We
prove that the search for better lower bounds can often
be turned into a problem of solving a large series of
linear programming instances. Implementing a
small-scale theorem prover based on these results, we
extract new human-readable time lower bounds for
several problems and identify patterns that allow for
further generalization. The framework can also be used
to prove concrete limitations on the current
techniques.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Ron:2013:ANR,
author = "Dana Ron and Gilad Tsur",
title = "On Approximating the Number of Relevant Variables in a
Function",
journal = j-TOCT,
volume = "5",
number = "2",
pages = "7:1--7:??",
month = jul,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2493246.2493250",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:08 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "In this work we consider the problem of approximating
the number of relevant variables in a function given
query access to the function. Since obtaining a
multiplicative factor approximation is hard in general,
we consider several relaxations of the problem. In
particular, we consider a relaxation of the property
testing variant of the problem and we consider
relaxations in which we have a promise that the
function belongs to a certain family of functions
(e.g., linear functions). In the former relaxation the
task is to distinguish between the case that the number
of relevant variables is at most $k$, and the case in
which it is far from any function in which the number
of relevant variables is more than $ (1 + \gamma) k $
for a parameter $ \gamma $. We give both upper bounds
and almost matching lower bounds for the relaxations we
study.",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Allender:2013:ISI,
author = "Eric Allender and Shafi Goldwasser",
title = "Introduction to the special issue on innovations in
theoretical computer science 2012",
journal = j-TOCT,
volume = "5",
number = "3",
pages = "8:1--8:??",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1145/2493252.2493253",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:12 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
note = "Special issue on innovations in theoretical computer
science 2012.",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Pagh:2013:CMM,
author = "Rasmus Pagh",
title = "Compressed matrix multiplication",
journal = j-TOCT,
volume = "5",
number = "3",
pages = "9:1--9:??",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1145/2493252.2493254",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:12 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
note = "Special issue on innovations in theoretical computer
science 2012.",
abstract = "We present a simple algorithm that approximates the
product of $n$-by-$n$ real matrices $A$ and $B$. Let $
|| A B ||_F $ denote the Frobenius norm of $ A B $, and
$b$ be a parameter determining the time\slash accuracy
trade-off. Given $2$-wise independent hash functions $
h_1, h_2 : [n] \to [b] $, and $ s_1, s_2 : [n] \to \{ -
1, + 1 \} $ the algorithm works by first
``compressing'' the matrix product into the polynomial
$ p (x) = \Sigma_{k = 1}^n \left (\Sigma_{i = 1}^n
A_{ik} s_1 (i) x^{h 1 (i)} \right) \left (\Sigma_{j =
1}^n B_{kj} s_2 (j) x^{h 2 (j)} \right) $. Using the
fast Fourier transform to compute polynomial
multiplication, we can compute $ c_0, \ldots {}, c_{b -
1} $ such that $ \Sigma_i c_i x^i = (p (x) \bmod x^b) +
(p (x) \div x^b) $ in time $ {\~ O}(n^2 + n b) $. An
unbiased estimator of $ (A B)_{ij} $ with variance at
most $ || A B ||_F^2 / b $ can then be computed as: $
C_{ij} = s_1 (i) s_2 (j) c_{(h_1 (i) + h_2 (j)) \bmod
b} $. Our approach also leads to an algorithm for
computing AB exactly, with high probability, in time $
{\~ O}(N + n b) $ in the case where $A$ and $B$ have at
most $N$ nonzero entries, and $ A B $ has at most $b$
nonzero entries.",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Viderman:2013:LTD,
author = "Michael Viderman",
title = "Linear-time decoding of regular expander codes",
journal = j-TOCT,
volume = "5",
number = "3",
pages = "10:1--10:??",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1145/2493252.2493255",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:12 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
note = "Special issue on innovations in theoretical computer
science 2012.",
abstract = "Sipser and Spielman (IEEE IT, [1996]) showed that any
$ (c, d) $-regular expander code with expansion
parameter $ > 3 / 4 $ is decodable in linear time from
a constant fraction of errors. Feldman et al. (IEEE IT,
[2007]) proved that expansion parameter $ > 2 / 3 + (1
/ 3) c $ is sufficient to correct a constant fraction
of errors in polynomial time using LP decoding. In this
work, we give a simple combinatorial algorithm that
achieves even better parameters. In particular, our
algorithm runs in linear time and works for any
expansion parameter $ > 2 / 3 - (1 / 6) c $. We also
prove that our decoding algorithm can be executed in
logarithmic time on a linear number of parallel
processors.",
acknowledgement = ack-nhfb,
articleno = "10",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Ozols:2013:QRS,
author = "Maris Ozols and Martin Roetteler and J{\'e}r{\'e}mie
Roland",
title = "Quantum rejection sampling",
journal = j-TOCT,
volume = "5",
number = "3",
pages = "11:1--11:??",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1145/2493252.2493256",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:12 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
note = "Special issue on innovations in theoretical computer
science 2012.",
abstract = "Rejection sampling is a well-known method to sample
from a target distribution, given the ability to sample
from a given distribution. The method has been first
formalized by von Neumann [1951] and has many
applications in classical computing. We define a
quantum analogue of rejection sampling: given a black
box producing a coherent superposition of (possibly
unknown) quantum states with some amplitudes, the
problem is to prepare a coherent superposition of the
same states, albeit with different target amplitudes.
The main result of this article is a tight
characterization of the query complexity of this
quantum state generation problem. We exhibit an
algorithm, which we call quantum rejection sampling,
and analyze its cost using semidefinite programming.
Our proof of a matching lower bound is based on the
automorphism principle that allows to symmetrize any
algorithm over the automorphism group of the problem.
Our main technical innovation is an extension of the
automorphism principle to continuous groups that arise
for quantum state generation problems where the oracle
encodes unknown quantum states, instead of just
classical data. Furthermore, we illustrate how quantum
rejection sampling may be used as a primitive in
designing quantum algorithms, by providing three
different applications. We first show that it was
implicitly used in the quantum algorithm for linear
systems of equations by Harrow et al. [2009]. Second we
show that it can be used to speed up the main step in
the quantum Metropolis sampling algorithm by Temme et
al. [2011]. Finally, we derive a new quantum algorithm
for the hidden shift problem of an arbitrary Boolean
function and relate its query complexity to
``water-filling'' of the Fourier spectrum.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Drucker:2013:HCP,
author = "Andrew Drucker",
title = "High-confidence predictions under adversarial
uncertainty",
journal = j-TOCT,
volume = "5",
number = "3",
pages = "12:1--12:??",
month = aug,
year = "2013",
DOI = "https://doi.org/10.1145/2493252.2493257",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:12 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
note = "Special issue on innovations in theoretical computer
science 2012.",
abstract = "We study the setting in which the bits of an unknown
infinite binary sequence $x$ are revealed sequentially
to an observer. We show that very limited assumptions
about $x$ allow one to make successful predictions
about unseen bits of $x$. First, we study the problem
of successfully predicting a single 0 from among the
bits of $x$. In our model, we have only one chance to
make a prediction, but may do so at a time of our
choosing. This model is applicable to a variety of
situations in which we want to perform an action of
fixed duration, and need to predict a ``safe''
time-interval to perform it. Letting $ N_t $ denote the
number of $1$'s among the first $t$ bits of $x$, we say
that $x$ is ``$ \epsilon $-weakly sparse'' if $ \lim
\inf (N_t / t) < = \epsilon $. Our main result is a
randomized algorithm that, given any $ \epsilon
$-weakly sparse sequence $x$, predicts a $0$ of $x$
with success probability as close as desired to $ 1 -
\epsilon $. Thus, we can perform this task with
essentially the same success probability as under the
much stronger assumption that each bit of $x$ takes the
value $1$ independently with probability $ \epsilon $.
We apply this result to show how to successfully
predict a bit ($0$ or $1$ ) under a broad class of
possible assumptions on the sequence $x$. The
assumptions are stated in terms of the behavior of a
finite automaton $M$ reading the bits of $x$. We also
propose and solve a variant of the well-studied
``ignorant forecasting'' problem. For every $ \epsilon
> 0 $, we give a randomized forecasting algorithm $
S_\epsilon $ that, given sequential access to a binary
sequence $x$, makes a prediction of the form: ``A $p$
fraction of the next $N$ bits will be $1$'s.'' (The
algorithm gets to choose $p$, $N$, and the time of the
prediction.) For any fixed sequence $x$, the forecast
fraction $p$ is accurate to within $ \pm {} \epsilon $
with probability $ 1 - \epsilon $.",
acknowledgement = ack-nhfb,
articleno = "12",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Chattopadhyay:2013:GIA,
author = "Arkadev Chattopadhyay and Jacobo Tor{\'a}n and Fabian
Wagner",
title = "Graph Isomorphism is Not {AC$^0$}-Reducible to Group
Isomorphism",
journal = j-TOCT,
volume = "5",
number = "4",
pages = "13:1--13:??",
month = nov,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2540088",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:15 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We give a new upper bound for the Group and Quasigroup
Isomorphism problems when the input structures are
given explicitly by multiplication tables. We show that
these problems can be computed by polynomial size
nondeterministic circuits of unbounded fan-in with $
O(\log \log n) $ depth and $ O(\log^2 n) $
nondeterministic bits, where n is the number of group
elements. This improves the existing upper bound for
the problems. In the previous bound the circuits have
bounded fan-in but depth $ O(\log^2 n) $ and also $
O(\log^2 n) $ nondeterministic bits. We then prove that
the kind of circuits from our upper bound cannot
compute the Parity function. Since Parity is
AC$^0$-reducible to Graph Isomorphism, this implies
that Graph Isomorphism is strictly harder than Group or
Quasigroup Isomorphism under the ordering defined by
AC$^0$ reductions. We extend this result to the
stronger ACC$^0 [p]$ reduction and its randomized
version.",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{De:2013:EOH,
author = "Anindya De and Elchanan Mossel",
title = "Explicit Optimal Hardness via {Gaussian} Stability
Results",
journal = j-TOCT,
volume = "5",
number = "4",
pages = "14:1--14:??",
month = nov,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2505766",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:15 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The results of Raghavendra [2008] show that assuming
Khot's Unique Games Conjecture [2002], for every
constraint satisfaction problem there exists a generic
semidefinite program that achieves the optimal
approximation factor. This result is existential as it
does not provide an explicit optimal rounding procedure
nor does it allow to calculate exactly the Unique Games
hardness of the problem. Obtaining an explicit optimal
approximation scheme and the corresponding
approximation factor is a difficult challenge for each
specific approximation problem. Khot et al. [2004]
established a general approach for determining the
exact approximation factor and the corresponding
optimal rounding algorithm for any given constraint
satisfaction problem. However, this approach crucially
relies on results explicitly proving optimal partitions
in the Gaussian space. Until recently, Borell's result
[1985] was the only nontrivial Gaussian partition
result known. In this article we derive the first
explicit optimal approximation algorithm and the
corresponding approximation factor using a new result
on Gaussian partitions due to Isaksson and Mossel
[2012]. This Gaussian result allows us to determine the
exact Unique Games Hardness of MAX-$3$-EQUAL. In
particular, our results show that Zwick's algorithm for
this problem achieves the optimal approximation factor
and prove that the approximation achieved by the
algorithm is $ \approx 0.796 $ as conjectured by Zwick
[1998]. We further use the previously known optimal
Gaussian partitions results to obtain a new Unique
Games Hardness factor for MAX-$k$-CSP: Using the
well-known fact that jointly normal pairwise
independent random variables are fully independent, we
show that the UGC hardness of Max-$k$-CSP is $ \lceil
(k + 1) / 2 \rceil 2^{k - 1} $, improving on results of
Austrin and Mossel [2009].",
acknowledgement = ack-nhfb,
articleno = "14",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Dalmau:2013:RSC,
author = "V{\'\i}ctor Dalmau and Andrei Krokhin",
title = "Robust Satisfiability for {CSPs}: Hardness and
Algorithmic Results",
journal = j-TOCT,
volume = "5",
number = "4",
pages = "15:1--15:??",
month = nov,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2540090",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:15 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "An algorithm for a constraint satisfaction problem is
called robust if it outputs an assignment satisfying at
least a $ (1 - f (\epsilon)) $-fraction of constraints
for each $ (1 - \epsilon) $-satisfiable instance (i.e.,
such that at most a \epsilon -fraction of constraints
needs to be removed to make the instance satisfiable),
where $ f(\epsilon) \to 0 $ as $ \epsilon \to 0 $. We
establish an algebraic framework for analyzing
constraint satisfaction problems admitting an efficient
robust algorithm with functions $f$ of a given growth
rate. We use this framework to derive hardness results.
We also describe three classes of problems admitting an
efficient robust algorithm such that $f$ is $ O (1 /
\log (1 / \epsilon)) $, $ O(\epsilon^{1 / k}) $ for
some $ k > 1 $, and $ O(\epsilon) $, respectively.
Finally, we give a complete classification of robust
satisfiability with a given $f$ for the Boolean case.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Fellows:2013:DFP,
author = "Michael Fellows and Fedor V. Fomin and Daniel
Lokshtanov and Elena Losievskaja and Frances Rosamond
and Saket Saurabh",
title = "Distortion is Fixed Parameter Tractable",
journal = j-TOCT,
volume = "5",
number = "4",
pages = "16:1--16:??",
month = nov,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2489789",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:15 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We study low-distortion embedding of metric spaces
into the line, and more generally, into the shortest
path metric of trees, from the parameterized complexity
perspective. Let $ M = M (G) $ be the shortest path
metric of an edge-weighted graph $G$, with the vertex
set $ V (G) $ and the edge set $ E (G) $, on $n$
vertices. We give the first fixed parameter tractable
algorithm that for an unweighted graph metric $M$ and
integer $d$ either constructs an embedding of $M$ into
the line with distortion at most $d$, or concludes that
no such embedding exists. Our algorithm requires O(
nd$^4$ (2 d + 1)$^{2d}$ ) time which is a significant
improvement over the best previous algorithm that runs
in time $ O(n^{4d + 2} d^{O(1)}) $. Because of its
apparent similarity to the notoriously hard Bandwidth
Minimization problem, we find it surprising that this
problem turns out to be fixed parameter tractable. We
extend our results on embedding unweighted graph metric
into the line in two ways. First, we give an algorithm
to construct small-distortion embeddings of weighted
graph metrics. The running time of our algorithm is $
O(n (d W)^4 (2 d + 1)^{2dW}) $, where $W$ is the
largest edge weight of the input graph. To complement
this result, we show that the exponential dependence on
the maximum edge weight is unavoidable. In particular,
we show that deciding whether a weighted graph metric $
M (G) $ with maximum weight $ W < | V (G)| $ can be
embedded into the line with distortion at most $d$ is
NP-complete for every fixed rational $ d \geq 2 $. This
rules out any possibility of an algorithm with running
time $ O((n W)^{h(d)}) $ where $h$ is a function of $d$
alone. Second, we consider more general host metrics
for which analogous results hold. In particular, we
prove that for any tree $T$ with maximum degree \Delta,
embedding $M$ into a shortest path metric of $T$ is
fixed parameter tractable, parameterized by $ (\Delta,
d) $.",
acknowledgement = ack-nhfb,
articleno = "16",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Razborov:2013:RA,
author = "Alexander Razborov and Emanuele Viola",
title = "Real Advantage",
journal = j-TOCT,
volume = "5",
number = "4",
pages = "17:1--17:??",
month = nov,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2540089",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:15 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We highlight the challenge of proving correlation
bounds between boolean functions and real-valued
polynomials, where any non-boolean output counts
against correlation. We prove that real-valued
polynomials of degree $ 1 2 \lg_2 \lg_2 n $ have
correlation with parity at most zero. Such a result is
false for modular and threshold polynomials. Its proof
is based on a variant of an anti-concentration result
by Costello et al. [2006].",
acknowledgement = ack-nhfb,
articleno = "17",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Harkins:2013:ELA,
author = "Ryan C. Harkins and John M. Hitchcock",
title = "Exact Learning Algorithms, Betting Games, and Circuit
Lower Bounds",
journal = j-TOCT,
volume = "5",
number = "4",
pages = "18:1--18:??",
month = nov,
year = "2013",
CODEN = "????",
DOI = "https://doi.org/10.1145/2539126.2539130",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Dec 12 17:32:15 MST 2013",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "This article extends and improves the work of Fortnow
and Klivans [2009], who showed that if a circuit class
$C$ has an efficient learning algorithm in Angluin's
model of exact learning via equivalence and membership
queries [Angluin 1988], then we have the lower bound
EXP$^{NP}$ not $C$. We use entirely different
techniques involving betting games [Buhrman et al.
2001] to remove the NP oracle and improve the lower
bound to EXP not $C$. This shows that it is even more
difficult to design a learning algorithm for $C$ than
the results of Fortnow and Klivans [2009] indicated. We
also investigate the connection between betting games
and natural proofs, and as a corollary the existence of
strong pseudorandom generators. Our results also yield
further evidence that the class of Boolean circuits has
no efficient exact learning algorithm. This is because
our separation is strong in that it yields a natural
proof [Razborov and Rudich 1997] against the class.
From this we conclude that an exact learning algorithm
for Boolean circuits would imply that strong
pseudorandom generators do not exist, which contradicts
widely believed conjectures from cryptography. As a
corollary we obtain that if strong pseudorandom
generators exist, then there is no exact learning
algorithm for Boolean circuits.",
acknowledgement = ack-nhfb,
articleno = "18",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Ada:2014:HBP,
author = "Anil Ada and Arkadev Chattopadhyay and Stephen A. Cook
and Lila Fontes and Michal Kouck{\'y} and Toniann
Pitassi",
title = "The Hardness of Being Private",
journal = j-TOCT,
volume = "6",
number = "1",
pages = "1:1--1:??",
month = mar,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2567671",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Apr 1 06:02:31 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Kushilevitz [1989] initiated the study of
information-theoretic privacy within the context of
communication complexity. Unfortunately, it has been
shown that most interesting functions are not privately
computable [Kushilevitz 1989, Brandt and Sandholm
2008]. The unattainability of perfect privacy for many
functions motivated the study of approximate privacy.
Feigenbaum et al. [2010a, 2010b] define notions of
worst-case as well as average-case approximate privacy
and present several interesting upper bounds as well as
some open problems for further study. In this article,
we obtain asymptotically tight bounds on the trade-offs
between both the worst-case and average-case
approximate privacy of protocols and their
communication cost for Vickrey auctions. Further, we
relate the notion of average-case approximate privacy
to other measures based on information cost of
protocols. This enables us to prove exponential lower
bounds on the subjective approximate privacy of
protocols for computing the Intersection function,
independent of its communication cost. This proves a
conjecture of Feigenbaum et al. [2010a].",
acknowledgement = ack-nhfb,
articleno = "1",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Austrin:2014:NNH,
author = "Per Austrin and Ryan O'Donnell and Li-Yang Tan and
John Wright",
title = "New {NP}-Hardness Results for $3$-Coloring and
$2$-to-$1$ Label Cover",
journal = j-TOCT,
volume = "6",
number = "1",
pages = "2:1--2:??",
month = mar,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2537800",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Apr 1 06:02:31 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We show that given a 3-colorable graph, it is NP-hard
to find a 3-coloring with $ (16 / 17 + \epsilon) $ of
the edges bichromatic. In a related result, we show
that given a satisfiable instance of the 2-to-1 Label
Cover problem, it is NP-hard to find a $ (23 / 24 +
\epsilon) $-satisfying assignment.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Glasser:2014:UDN,
author = "Christian Gla{\ss}er and John M. Hitchcock and A.
Pavan and Stephan Travers",
title = "Unions of Disjoint {NP}-Complete Sets",
journal = j-TOCT,
volume = "6",
number = "1",
pages = "3:1--3:??",
month = mar,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2591508",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Apr 1 06:02:31 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We study the following question: if A and B are
disjoint NP-complete sets, then is A \cup B
NP-complete? We provide necessary and sufficient
conditions under which the union of disjoint
NP-complete sets remain complete.",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Sun:2014:ECN,
author = "Shu-Ming Sun and Ning Zhong",
title = "On Effective Convergence of Numerical Solutions for
Differential Equations",
journal = j-TOCT,
volume = "6",
number = "1",
pages = "4:1--4:??",
month = mar,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2578219",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Apr 1 06:02:31 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "This article studies the effective convergence of
numerical solutions of initial value problems (IVPs)
for ordinary differential equations (ODEs). A
convergent sequence $ \{ Y_m \} $ of numerical
solutions is said to be effectively convergent to the
exact solution if there is an algorithm that computes
an $ N \in N $, given an arbitrary $ n \in N $ as
input, such that the error between $ Y_m $ and the
exact solution is less than $ 2^{-n} $ for all $ m \geq
N $. It is proved that there are convergent numerical
solutions generated from Euler's method which are not
effectively convergent. It is also shown that a
theoretically-proved-computable solution using Picard's
iteration method might not be computable by classical
numerical methods, which suggests that sometimes there
is a gap between theoretical computability and
practical numerical computations concerning solutions
of ODEs. Moreover, it is noted that the main theorem
(Theorem 4.1) provides an example of an IVP with a
nonuniform Lipschitz function for which the numerical
solutions generated by Euler's method are still
convergent.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{ODonnell:2014:OLB,
author = "Ryan O'Donnell and Yi Wu and Yuan Zhou",
title = "Optimal Lower Bounds for Locality-Sensitive Hashing
(Except When $q$ is Tiny)",
journal = j-TOCT,
volume = "6",
number = "1",
pages = "5:1--5:??",
month = mar,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2578221",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Apr 1 06:02:31 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/hash.bib;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We study lower bounds for Locality-Sensitive Hashing
(LSH) in the strongest setting: point sets in $ \{ 0, 1
\}^d $ under the Hamming distance. Recall that $H$ is
said to be an $ (r, c r, p, q) $-sensitive hash family
if all pairs $ x, y \in \{ 0, 1 \}^d $ with $ {\rm
dist}(x, y) \leq r $ have probability at least $p$ of
collision under a randomly chosen $ h \in H $, whereas
all pairs $ x, y \in \{ 0, 1 \}^d $ with $ {\rm
dist}(x, y) \geq c r $ have probability at most $q$ of
collision. Typically, one considers $ d \to \infty $,
with $ c > 1 $ fixed and $q$ bounded away from $0$. For
its applications to approximate nearest-neighbor search
in high dimensions, the quality of an LSH family $H$ is
governed by how small its $ \rho $ parameter $ \rho =
\ln (1 / p) / l n(1 / q) $ is as a function of the
parameter $c$. The seminal paper of Indyk and Motwani
[1998] showed that for each $ c \geq 1 $, the extremely
simple family $ H = \{ x \mapsto x $ _i$ : i \in [d] \}
$ achieves $ \rho \leq 1 / c $. The only known lower
bound, due to Motwani et al. [2007], is that $ \rho $
must be at least $ (e^{1 / c} - 1) / (e^{1 / c} + 1)
\geq .46 / c $ (minus $ o_d(1) $ ). The contribution of
this article is twofold. (1) We show the ``optimal''
lower bound for $ \rho $: it must be at least $ 1 / c $
(minus $ o_d(1) $ ). Our proof is very simple,
following almost immediately from the observation that
the noise stability of a boolean function at time $t$
is a log-convex function of $t$. (2) We raise and
discuss the following issue: neither the application of
LSH to nearest-neighbor search nor the known LSH lower
bounds hold as stated if the q parameter is tiny. Here,
``tiny'' means $ q = 2^{- \Theta (d)} $, a parameter
range we believe is natural.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Cygan:2014:CCG,
author = "Marek Cygan and Stefan Kratsch and Marcin Pilipczuk
and Michal Pilipczuk and Magnus Wahlstr{\"o}m",
title = "Clique Cover and Graph Separation: New
Incompressibility Results",
journal = j-TOCT,
volume = "6",
number = "2",
pages = "6:1--6:??",
month = may,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2594439",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Jun 5 14:42:53 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The field of kernelization studies polynomial-time
preprocessing routines for hard problems in the
framework of parameterized complexity. In this article,
we show that, unless the polynomial hierarchy collapses
to its third level, the following parameterized
problems do not admit a polynomial-time preprocessing
algorithm that reduces the size of an instance to
polynomial in the parameter: ---Edge Clique Cover,
parameterized by the number of cliques, ---Directed
Edge/Vertex Multiway Cut, parameterized by the size of
the cutset, even in the case of two terminals,
---Edge/Vertex Multicut, parameterized by the size of
the cutset, and --- k -Way Cut, parameterized by the
size of the cutset.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Chen:2014:HIA,
author = "Yijia Chen and J{\"o}rg Flum and Moritz M{\"u}ller",
title = "Hard Instances of Algorithms and Proof Systems",
journal = j-TOCT,
volume = "6",
number = "2",
pages = "7:1--7:??",
month = may,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2601336",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Jun 5 14:42:53 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "If the class TAUT of tautologies of propositional
logic has no almost optimal algorithm, then every
algorithm A deciding TAUT has a hard sequence, that is,
a polynomial time computable sequence witnessing that A
is not almost optimal. We show that this result extends
to every $\Pi t p$-complete problem with $t \geq 1$;
however, assuming the Measure Hypothesis, there is a
problem which has no almost optimal algorithm but is
decided by an algorithm without hard sequences. For
problems Q with an almost optimal algorithm, we analyze
whether every algorithm deciding Q, which is not almost
optimal, has a hard sequence.",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Goldberg:2014:CAC,
author = "Leslie Ann Goldberg and Mark Jerrum",
title = "The Complexity of Approximately Counting Tree
Homomorphisms",
journal = j-TOCT,
volume = "6",
number = "2",
pages = "8:1--8:??",
month = may,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2600917",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Jun 5 14:42:53 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We study two computational problems, parameterised by
a fixed tree H. \#HOMSTO( H ) is the problem of
counting homomorphisms from an input graph G to H.
\#WHOMSTO( H ) is the problem of counting weighted
homomorphisms to H, given an input graph G and a weight
function for each vertex v of G. Even though H is a
tree, these problems turn out to be sufficiently rich
to capture all of the known approximation behaviour in
\# P. We give a complete trichotomy for \#WHOMSTO( H ).
If H is a star, then \#WHOMSTO( H ) is in FP. If H is
not a star but it does not contain a certain induced
subgraph J 3, then \#WHOMSTO( H ) is equivalent under
approximation-preserving (AP) reductions to \#BIS, the
problem of counting independent sets in a bipartite
graph. This problem is complete for the class \#RH \Pi
1 under AP-reductions. Finally, if H contains an
induced J$_3$, then \#WHOMSTO( H ) is equivalent under
AP-reductions to \#SAT, the problem of counting
satisfying assignments to a CNF Boolean formula. Thus,
\#WHOMSTO( H ) is complete for \#P under AP-reductions.
The results are similar for \#HOMSTO( H ) except that a
rich structure emerges if H contains an induced J$_3$.
We show that there are trees H for which \#HOMSTO( H )
is \# SAT -equivalent (disproving a plausible
conjecture of Kelk). However, it is still not known
whether \#HOMSTO( H ) is \#SAT-hard for every tree H
which contains an induced J 3. It turns out that there
is an interesting connection between these
homomorphism-counting problems and the problem of
approximating the partition function of the
ferromagnetic Potts model. In particular, we show that
for a family of graphs Jq, parameterised by a positive
integer q, the problem \#HOMSTO( Jq ) is
AP-interreducible with the problem of approximating the
partition function of the q -state Potts model. It was
not previously known that the Potts model had a
homomorphism-counting interpretation. We use this
connection to obtain some additional upper bounds for
the approximation complexity of \#HOMSTO( Jq ).",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Etessami:2014:NCC,
author = "Kousha Etessami and Alistair Stewart and Mihalis
Yannakakis",
title = "A Note on the Complexity of Comparing Succinctly
Represented Integers, with an Application to Maximum
Probability Parsing",
journal = j-TOCT,
volume = "6",
number = "2",
pages = "9:1--9:??",
month = may,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2601327",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Jun 5 14:42:53 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The following two decision problems capture the
complexity of comparing integers or rationals that are
succinctly represented in product-of-exponentials
notation, or equivalently, via arithmetic circuits
using only multiplication and division gates, and
integer inputs. Input instance: Four lists of positive
integers: a 1,\ldots{}, an \in N+ n; b 1,\ldots{}, bn
\in N+ n; c 1,\ldots{}, cm \in N+ m; d 1, \ldots{}, dm
\in N+ m; where each of the integers is represented in
binary. Problem 1 (equality testing): Decide whether
$a_1 b_1 a_2 b_2 \cdots a_n b_n = c_1 d_1 c_2 d_2
\cdots c_m d_m$. Problem 2 (inequality testing): Decide
whether $a_1 b_1 a_2 b_2 \cdots a_n b_n \geq c_1 d_1
c_2 d_2 \cdots c_m d_m$. Problem 1 is easily decidable
in polynomial time using a simple iterative
algorithm. Problem 2 is much harder. We observe that
the complexity of Problem 2 is intimately connected to
deep conjectures and results in number theory. In
particular, if a refined form of the ABC conjecture
formulated by Baker in 1998 holds, or if the older
Lang-Waldschmidt conjecture (formulated in 1978) on
linear forms in logarithms holds, then Problem 2 is
decidable in P-time (in the standard Turing model of
computation). Moreover, it follows from the best
available quantitative bounds on linear forms in
logarithms, namely, by Baker and W{\"u}stholz [1993] or
Matveev [2000], that if m and n are fixed universal
constants then Problem 2 is decidable in P-time
(without relying on any conjectures). This latter fact
was observed earlier by Shub [1993]. We describe one
application: P-time maximum probability parsing for
arbitrary stochastic context-free grammars (where
\epsilon -rules are allowed).",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Allender:2014:ISI,
author = "Eric Allender and Shafi Goldwasser",
title = "Introduction to the Special Issue on Innovations in
Theoretical Computer Science 2012 --- {Part II}",
journal = j-TOCT,
volume = "6",
number = "3",
pages = "10:1--10:??",
month = jul,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2638595",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Oct 1 16:40:04 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
acknowledgement = ack-nhfb,
articleno = "10",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
remark = "Special issue on innovations in theoretical computer
science 2012 --- Part II.",
}
@Article{Kanade:2014:LHS,
author = "Varun Kanade and Thomas Steinke",
title = "Learning Hurdles for Sleeping Experts",
journal = j-TOCT,
volume = "6",
number = "3",
pages = "11:1--11:??",
month = jul,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2505983",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Oct 1 16:40:04 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We study the online decision problem in which the set
of available actions varies over time, also called the
sleeping experts problem. We consider the setting in
which the performance comparison is made with respect
to the best ordering of actions in hindsight. In this
article, both the payoff function and the availability
of actions are adversarial. Kleinberg et al. [2010]
gave a computationally efficient no-regret algorithm in
the setting in which payoffs are stochastic. Kanade et
al. [2009] gave an efficient no-regret algorithm in the
setting in which action availability is stochastic.
However, the question of whether there exists a
computationally efficient no-regret algorithm in the
adversarial setting was posed as an open problem by
Kleinberg et al. [2010]. We show that such an algorithm
would imply an algorithm for PAC learning DNF, a
long-standing important open problem. We also consider
the setting in which the number of available actions is
restricted and study its relation to agnostic-learning
monotone disjunctions over examples with bounded
Hamming weight.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
remark = "Special issue on innovations in theoretical computer
science 2012 --- Part II.",
}
@Article{Valiant:2014:ERF,
author = "Paul Valiant",
title = "Evolvability of Real Functions",
journal = j-TOCT,
volume = "6",
number = "3",
pages = "12:1--12:??",
month = jul,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2633598",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Oct 1 16:40:04 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We formulate a notion of evolvability for functions
with domain and range that are real-valued vectors, a
compelling way of expressing many natural biological
processes. We show that linear and fixed-degree
polynomial functions are evolvable in the following
dually-robust sense: There is a single evolution
algorithm that, for all convex loss functions,
converges for all distributions. It is possible that
such dually-robust results can be achieved by simpler
and more-natural evolution algorithms. Towards this
end, we introduce a simple and natural algorithm that
we call wide-scale random noise and prove a
corresponding result for the L$_2$ metric. We
conjecture that the algorithm works for a more general
class of metrics.",
acknowledgement = ack-nhfb,
articleno = "12",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
remark = "Special issue on innovations in theoretical computer
science 2012 --- Part II.",
}
@Article{Brakerski:2014:LFH,
author = "Zvika Brakerski and Craig Gentry and Vinod
Vaikuntanathan",
title = "(Leveled) Fully Homomorphic Encryption without
Bootstrapping",
journal = j-TOCT,
volume = "6",
number = "3",
pages = "13:1--13:??",
month = jul,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2633600",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Oct 1 16:40:04 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We present a novel approach to fully homomorphic
encryption (FHE) that dramatically improves performance
and bases security on weaker assumptions. A central
conceptual contribution in our work is a new way of
constructing leveled, fully homomorphic encryption
schemes (capable of evaluating arbitrary
polynomial-size circuits of a-priori bounded depth),
without Gentry's bootstrapping procedure. Specifically,
we offer a choice of FHE schemes based on the learning
with error (LWE) or Ring LWE (RLWE) problems that have
2 \lambda security against known attacks. We construct
the following. (1) A leveled FHE scheme that can
evaluate depth-$L$ arithmetic circuits (composed of
fan-in 2 gates) using $O(\lambda . L 3)$ per-gate
computation, quasilinear in the security
parameter. Security is based on RLWE for an
approximation factor exponential in $L$. This
construction does not use the bootstrapping
procedure. (2) A leveled FHE scheme that can evaluate
depth-$L$ arithmetic circuits (composed of fan-in 2
gates) using $O (\lambda 2)$ per-gate computation,
which is independent of $L$. Security is based on RLWE
for quasipolynomial factors. This construction uses
bootstrapping as an optimization. We obtain similar
results for LWE, but with worse performance. All
previous (leveled) FHE schemes required a per-gate
computation of \Omega (\lambda 3.5), and all of them
relied on subexponential hardness assumptions. We
introduce a number of further optimizations to our
scheme based on the Ring LWE assumption. As an example,
for circuits of large width (e.g., where a constant
fraction of levels have width $ \Omega (\lambda)$), we
can reduce the per-gate computation of the bootstrapped
version to $O (\lambda)$, independent of $L$, by
batching the bootstrapping operation. At the core of
our construction is a new approach for managing the
noise in lattice-based ciphertexts, significantly
extending the techniques of Brakerski and
Vaikuntanathan [2011b].",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
remark = "Special issue on innovations in theoretical computer
science 2012 --- Part II.",
}
@Article{Cook:2014:OWF,
author = "James Cook and Omid Etesami and Rachel Miller and Luca
Trevisan",
title = "On the One-Way Function Candidate Proposed by
{Goldreich}",
journal = j-TOCT,
volume = "6",
number = "3",
pages = "14:1--14:??",
month = jul,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2633602",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Oct 1 16:40:04 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Goldreich [2000] proposed a candidate one-way function
based on a bipartite graph of small right-degree d,
where the vertices on the left (resp. right) represent
input (resp. output) bits of the function. Each output
bit is computed by evaluating a fixed d -ary binary
predicate on the input bits adjacent to that output
bit. We study this function when the predicate is
random or depends linearly on many of its input bits.
We assume that the graph is a random balanced bipartite
graph with right-degree d. Inverting this function as a
one-way function by definition means finding an element
in the preimage of output of this function for a random
input. We bound the expected size of this preimage.
Next, using the preceding bound, we prove that two
restricted types of backtracking algorithms called
myopic and drunk backtracking algorithms with high
probability take exponential time to invert the
function, even if we allow the algorithms to use DPLL
elimination rules. (For drunk algorithms, a similar
result was proved by Itsykson [2010].) We also ran a
SAT solver on the satisfiability problem equivalent to
the problem of inverting the function, and
experimentally observed an exponential increase in
running time as a function of the input length.",
acknowledgement = ack-nhfb,
articleno = "14",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
remark = "Special issue on innovations in theoretical computer
science 2012 --- Part II.",
}
@Article{Cook:2014:CCC,
author = "Stephen A. Cook and Yuval Filmus and Dai Tri Man
L{\^e}",
title = "The complexity of the comparator circuit value
problem",
journal = j-TOCT,
volume = "6",
number = "4",
pages = "15:1--15:??",
month = aug,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2635822",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Aug 18 17:06:20 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "In 1990, Subramanian [1990] defined the complexity
class CC as the set of problems log-space reducible to
the comparator circuit value problem (CCV). He and Mayr
showed that NL $ \subseteq $ CC $ \subseteq $ P, and
proved that in addition to CCV several other problems
are complete for CC, including the stable marriage
problem, and finding the lexicographically first
maximal matching in a bipartite graph. Although the
class has not received much attention since then, we
are interested in CC because we conjecture that it is
incomparable with the parallel class NC which also
satisfies NL $ \subseteq $ NC $ \subseteq $ P, and note
that this conjecture implies that none of the
CC-complete problems has an efficient polylog time
parallel algorithm. We provide evidence for our
conjecture by giving oracle settings in which
relativized CC and relativized NC are incomparable. We
give several alternative definitions of CC, including
(among others) the class of problems computed by
uniform polynomial-size families of comparator circuits
supplied with copies of the input and its negation, the
class of problems AC0-reducible to Ccv, and the class
of problems computed by uniform AC0 circuits with AXccv
gates. We also give a machine model for CC, which
corresponds to its characterization as log-space
uniform polynomial-size families of comparator
circuits. These various characterizations show that CC
is a robust class. Our techniques also show that the
corresponding function class FCC is closed under
composition. The main technical tool we employ is
universal comparator circuits. Other results include a
simpler proof of NL $ \subseteq $ CC, a more careful
analysis showing the lexicographically first maximal
matching problem and its variants are CC-complete under
AC0 many-one reductions, and an explanation of the
relation between the Gale--Shapley algorithm and
Subramanian's algorithm for stable marriage. This
article continues the previous work of Cook et al.
[2011], which focused on Cook-Nguyen style uniform
proof complexity, answering several open questions
raised in that article.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Fellows:2014:FCU,
author = "Michael R. Fellows and Bart M. P. Jansen",
title = "{FPT} is characterized by useful obstruction sets:
Connecting algorithms, kernels, and quasi-orders",
journal = j-TOCT,
volume = "6",
number = "4",
pages = "16:1--16:??",
month = aug,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2635820",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Aug 18 17:06:20 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Many graph problems were first shown to be
fixed-parameter tractable using the results of
Robertson and Seymour on graph minors. We show that the
combination of finite, computable obstruction sets and
efficient order tests is not just one way of obtaining
strongly uniform FPT algorithms, but that all of FPT
may be captured in this way. Our new characterization
of FPT has a strong connection to the theory of
kernelization, as we prove that problems with
polynomial kernels can be characterized by obstruction
sets whose elements have polynomial size. Consequently
we investigate the interplay between the sizes of
problem kernels and the sizes of the elements of such
obstruction sets, obtaining several examples of how
results in one area yield new insights in the other. We
show how exponential-size minor-minimal obstructions
for pathwidth $k$ form the crucial ingredient in a
novel or-cross-composition for $k$-Pathwidth,
complementing the trivial and-composition that is known
for this problem. In the other direction, we show that
or-cross-compositions into a parameterized problem can
be used to rule out the existence of efficiently
generated quasi-orders on its instances that
characterize the no-instances by polynomial-size
obstructions.",
acknowledgement = ack-nhfb,
articleno = "16",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Gobel:2014:CCH,
author = "Andreas G{\"o}bel and Leslie Ann Goldberg and David
Richerby",
title = "The complexity of counting homomorphisms to cactus
graphs modulo 2",
journal = j-TOCT,
volume = "6",
number = "4",
pages = "17:1--17:??",
month = aug,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2635825",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Aug 18 17:06:20 MDT 2014",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "A homomorphism from a graph $G$ to a graph $H$ is a
function from $ V(G)$ to $ V(H)$ that preserves edges.
Many combinatorial structures that arise in mathematics
and in computer science can be represented naturally as
graph homomorphisms and as weighted sums of graph
homomorphisms. In this article, we study the complexity
of counting homomorphisms modulo 2. The complexity of
modular counting was introduced by Papadimitriou and
Zachos and it has been pioneered by Valiant who
famously introduced a problem for which counting modulo
7 is easy but counting modulo 2 is intractable. Modular
counting provides a rich setting in which to study the
structure of homomorphism problems. In this case, the
structure of the graph $H$ has a big influence on the
complexity of the problem. Thus, our approach is
graph-theoretic. We give a complete solution for the
class of cactus graphs, which are connected graphs in
which every edge belongs to at most one cycle. Cactus
graphs arise in many applications such as the modelling
of wireless sensor networks and the comparison of
genomes. We show that, for some cactus graphs $H$,
counting homomorphisms to $H$ modulo 2 can be done in
polynomial time. For every other fixed cactus graph
$H$, the problem is complete in the complexity class $
\oplus P$, which is a wide complexity class to which
every problem in the polynomial hierarchy can be
reduced (using randomised reductions). Determining
which $H$ lead to tractable problems can be done in
polynomial time. Our result builds upon the work of
Faben and Jerrum, who gave a dichotomy for the case in
which $H$ is a tree.",
acknowledgement = ack-nhfb,
articleno = "17",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Watson:2014:ALB,
author = "Thomas Watson",
title = "Advice Lower Bounds for the Dense Model Theorem",
journal = j-TOCT,
volume = "7",
number = "1",
pages = "1:1--1:??",
month = dec,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2676659",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Jan 13 17:53:00 MST 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We prove a lower bound on the amount of nonuniform
advice needed by black-box reductions for the Dense
Model Theorem of Green, Tao, and Ziegler, and of
Reingold, Trevisan, Tulsiani, and Vadhan. The latter
theorem roughly says that for every distribution $D$
that is $ \delta $-dense in a distribution that is $
\epsilon '$-indistinguishable from uniform, there
exists a ``dense model'' for $D$, that is, a
distribution that is $ \delta $ -dense in the uniform
distribution and is $ \epsilon $-indistinguishable from
$D$. This $ \epsilon $-indistinguishability is with
respect to an arbitrary small class of functions $F$.
For the natural case where $ \epsilon ' \geq \Omega
(\epsilon \delta)$ and $ \epsilon \geq \delta O(1)$,
our lower bound implies that $ \Omega (\sqrt (1 /
\epsilon) \log (1 / \delta) \cdot \log | F |)$ advice
bits are necessary for a certain type of reduction that
establishes a stronger form of the Dense Model Theorem
(and which encompasses all known proofs of the Dense
Model Theorem in the literature). There is only a
polynomial gap between our lower bound and the best
upper bound for this case (due to Zhang), which is $ O
((1 / \epsilon^2) \log (1 / \delta) \cdot \log | F |)$.
Our lower bound can be viewed as an analogue of list
size lower bounds for list-decoding of error-correcting
codes, but for ``dense model decoding'' instead.",
acknowledgement = ack-nhfb,
articleno = "1",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Awasthi:2014:LLF,
author = "Pranjal Awasthi and Madhav Jha and Marco Molinaro and
Sofya Raskhodnikova",
title = "Limitations of Local Filters of {Lipschitz} and
Monotone Functions",
journal = j-TOCT,
volume = "7",
number = "1",
pages = "2:1--2:??",
month = dec,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2692372.2692373",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Jan 13 17:53:00 MST 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We study local filters for two properties of functions
of the form $ f : \{ 0, 1 d \} \to R $: the Lipschitz
property and monotonicity. A local filter with additive
error a is a randomized algorithm that is given
black-box access to a function $f$ and a query point
$x$ in the domain of $f$. It outputs a value $f$ (x)
such that (i) the reconstructed function $ f(x)$
satisfies the property (in our case, is Lipschitz or
monotone) and (ii) if the input function $f$ satisfies
the property, then for every point $x$ in the domain
(with high constant probability) the reconstructed
value $ F(x)$ differs from $ f(x)$ by at most $a$.
Local filters were introduced by Saks and Seshadhri
[2010]. The relaxed definition we study is due to
Bhattacharyya et al. [2012], except that we further
relax it by allowing additive error. Local filters for
Lipschitz and monotone functions have applications to
areas such as data privacy. We show that every local
filter for Lipschitz or monotone functions runs in time
exponential in the dimension d, even when the filter is
allowed significant additive error. Prior lower bounds
(for local filters with no additive error, that is,
with $ a = 0$) applied only to a more restrictive class
of filters, for example, nonadaptive filters. To prove
our lower bounds, we construct families of hard
functions and show that lookups of a local filter on
these functions are captured by a combinatorial object
that we call a $c$-connector. Then we present a lower
bound on the maximum outdegree of a $c$-connector and
show that it implies the desired bounds on the running
time of local filters. Our lower bounds, in particular,
imply the same bound on the running time for a class of
privacy mechanisms.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Greco:2014:CNC,
author = "Gianluigi Greco and Enrico Malizia and Luigi Palopoli
and Francesco Scarcello",
title = "The Complexity of the Nucleolus in Compact Games",
journal = j-TOCT,
volume = "7",
number = "1",
pages = "3:1--3:??",
month = dec,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2692372.2692374",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Jan 13 17:53:00 MST 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The nucleolus is a well-known solution concept for
coalitional games to fairly distribute the total
available worth among the players. The nucleolus is
known to be NP -hard to compute over compact
coalitional games, that is, over games whose functions
specifying the worth associated with each coalition are
encoded in terms of polynomially computable functions
over combinatorial structures. In particular, hardness
results have been exhibited over minimum spanning tree
games, threshold games, and flow games. However, due to
its intricate definition involving reasoning over
exponentially many coalitions, a nontrivial upper bound
on its complexity was missing in the literature and
looked for. This article faces this question and
precisely characterizes the complexity of the
nucleolus, by exhibiting an upper bound that holds on
any class of compact games, and by showing that this
bound is tight even on the (structurally simple) class
of graph games. The upper bound is established by
proposing a variant of the standard linear-programming
based algorithm for nucleolus computation and by
studying a framework for reasoning about succinctly
specified linear programs, which are contributions of
interest in their own. The hardness result is based on
an elaborate combinatorial reduction, which is
conceptually relevant for it provides a ``measure'' of
the computational cost to be paid for guaranteeing
voluntary participation to the distribution process. In
fact, the pre-nucleolus is known to be efficiently
computable over graph games, with this solution concept
being defined as the nucleolus but without guaranteeing
that each player is granted with it at least the worth
she can get alone, that is, without collaborating with
the other players. Finally, this article identifies
relevant tractable classes of coalitional games, based
on the notion of type of a player. Indeed, in most
applications where many players are involved, it is
often the case that such players do belong in fact to a
limited number of classes, which is known in advance
and may be exploited for computing the nucleolus in a
fast way.",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Kratsch:2014:KLB,
author = "Stefan Kratsch and Marcin Pilipczuk and Ashutosh Rai
and Venkatesh Raman",
title = "Kernel Lower Bounds using Co-Nondeterminism: Finding
Induced Hereditary Subgraphs",
journal = j-TOCT,
volume = "7",
number = "1",
pages = "4:1--4:??",
month = dec,
year = "2014",
CODEN = "????",
DOI = "https://doi.org/10.1145/2691321",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Jan 13 17:53:00 MST 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "This work further explores the applications of
co-nondeterminism for showing kernelization lower
bounds. The only known example prior to this work
excludes polynomial kernelizations for the so-called
Ramsey problem of finding an independent set or a
clique of at least $k$ vertices in a given graph
[Kratsch 2012]. We study the more general problem of
finding induced subgraphs on $k$ vertices fulfilling
some hereditary property $ \Pi $, called $ \Pi
$-Induced Subgraph. The problem is NP-hard for all
nontrivial choices of $ \Pi $ by a classic result of
Lewis and Yannakakis [1980]. The parameterized
complexity of this problem was classified by Khot and
Raman [2002] depending on the choice of $ \Pi $. The
interesting cases for kernelization are for $ \Pi $
containing all independent sets and all cliques, since
the problem is trivially polynomial time solvable or
W[1]-hard otherwise. Our results are twofold. Regarding
$ \Pi $-Induced Subgraph, we show that for a large
choice of natural graph properties $ \Pi $, including
chordal, perfect, cluster, and cograph, there is no
polynomial kernel with respect to $k$. This is
established by two theorems, each one capturing
different (but not necessarily exclusive) sets of
properties: one using a co-nondeterministic variant of
OR-cross-composition and one by a polynomial parameter
transformation from Ramsey. Additionally, we show how
to use improvement versions of NP-hard problems as
source problems for lower bounds, without requiring
their NP-hardness. For example, for $ \Pi $-Induced
Subgraph our compositions may assume existing solutions
of size $ k - 1$. This follows from the more general
fact that source problems for OR-(cross-)compositions
need only be NP-hard under co-nondeterministic
reductions. We believe this to be useful for further
lower-bound proofs, for example, since improvement
versions simplify the construction of a disjunction
(OR) of instances required in compositions. This adds a
second way of using co-nondeterminism for lower
bounds.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Filmus:2015:ELB,
author = "Yuval Filmus and Toniann Pitassi and Rahul Santhanam",
title = "Exponential Lower Bounds for {AC$0$-Frege} Imply
Superpolynomial {Frege} Lower Bounds",
journal = j-TOCT,
volume = "7",
number = "2",
pages = "5:1--5:??",
month = may,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2656209",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue May 12 06:02:22 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We give a general transformation that turns
polynomial-size Frege proofs into subexponential-size
AC$^0$-Frege proofs. This indicates that proving truly
exponential lower bounds for AC$^0$-Frege is hard, as
it is a long-standing open problem to prove
superpolynomial lower bounds for Frege. Our
construction is optimal for proofs of formulas of
unbounded depth. As a consequence of our main result,
we are able to shed some light on the question of
automatizability for bounded-depth Frege systems.
First, we present a simpler proof of the results of
Bonet et al. showing that under cryptographic
assumptions, bounded-depth Frege proofs are not
automatizable. Second, we show that because our proof
is more general, under the right cryptographic
assumptions, it could resolve the automatizability
question for lower-depth Frege systems.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Blaser:2015:SCT,
author = "Markus Bl{\"a}ser and Bodo Manthey",
title = "Smoothed Complexity Theory",
journal = j-TOCT,
volume = "7",
number = "2",
pages = "6:1--6:??",
month = may,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2656210",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue May 12 06:02:22 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Smoothed analysis is a new way of analyzing algorithms
introduced by Spielman and Teng. Classical methods like
worst-case or average-case analysis have accompanying
complexity classes, such as P and Avg-P, respectively.
Whereas worst-case or average-case analysis give us a
means to talk about the running time of a particular
algorithm, complexity classes allow us to talk about
the inherent difficulty of problems. Smoothed analysis
is a hybrid of worst-case and average-case analysis and
compensates some of their drawbacks. Despite its
success for the analysis of single algorithms and
problems, there is no embedding of smoothed analysis
into computational complexity theory, which is
necessary to classify problems according to their
intrinsic difficulty. We propose a framework for
smoothed complexity theory, define the relevant
classes, and prove some first hardness results (of
bounded halting and tiling) and tractability results
(binary optimization problems, graph coloring,
satisfiability) within this framework.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Chen:2015:FCC,
author = "Hubie Chen and Moritz M{\"u}ller",
title = "The Fine Classification of Conjunctive Queries and
Parameterized Logarithmic Space",
journal = j-TOCT,
volume = "7",
number = "2",
pages = "7:1--7:??",
month = may,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2751316",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue May 12 06:02:22 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We perform a fundamental investigation of the
complexity of conjunctive query evaluation from the
perspective of parameterized complexity. We classify
sets of Boolean conjunctive queries according to the
complexity of this problem. Previous work showed that a
set of conjunctive queries is fixed-parameter tractable
precisely when the set is equivalent to a set of
queries having bounded treewidth. We present a fine
classification of query sets up to parameterized
logarithmic space reduction. We show that, in the
bounded treewidth regime, there are three complexity
degrees and that the properties that determine the
degree of a query set are bounded pathwidth and bounded
tree depth. We also engage in a study of the two higher
degrees via logarithmic space machine characterizations
and complete problems. Our work yields a significantly
richer perspective on the complexity of conjunctive
queries and, at the same time, suggests new avenues of
research in parameterized complexity.",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Komarath:2015:PEB,
author = "Balagopal Komarath and Jayalal Sarma",
title = "Pebbling, Entropy, and Branching Program Size Lower
Bounds",
journal = j-TOCT,
volume = "7",
number = "2",
pages = "8:1--8:??",
month = may,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2751320",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue May 12 06:02:22 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We contribute to the program of proving lower bounds
on the size of branching programs solving the Tree
Evaluation Problem introduced by Cook et al. [2012].
Proving a superpolynomial lower bound for the size of
nondeterministic thrifty branching programs would be an
important step toward separating NL from P using the
tree evaluation problem. First, we show that Read-Once
Nondeterministic Thrifty BPs are equivalent to whole
black-white pebbling algorithms, thus showing a tight
lower bound (ignoring polynomial factors) for this
model. We then introduce a weaker restriction of
nondeterministic thrifty branching programs called
Bitwise Independence. The best known [Cook et al. 2012]
nondeterministic thrifty branching programs (of size $
O(k^{h / 2 + 1})$) for the tree evaluation problem are
Bitwise Independent. As our main result, we show that
any Bitwise Independent Nondeterministic Thrifty
Branching Program solving $ {\rm BT}_2 (h, k)$ must
have at least $ (k2)^{h / 2}$ states. Prior to this
work, lower bounds were known for nondeterministic
thrifty branching programs only for fixed heights $ h =
2, 3, 4$ [Cook et al. 2012]. We prove our results by
associating a fractional black-white pebbling strategy
with any bitwise independent nondeterministic thrifty
branching program solving the Tree Evaluation Problem.
Such a connection was not known previously, even for
fixed heights. Our main technique is the entropy method
introduced by Jukna and Z{\'a}k [2001] originally in
the context of proving lower bounds for read-once
branching programs. We also show that the previous
lower bounds known [Cook et al. 2012] for deterministic
branching programs for the Tree Evaluation Problem can
be obtained using this approach. Using this method, we
also show tight lower bounds for any $k$-way
deterministic branching program solving the Tree
Evaluation Problem when the instances are restricted to
have the same group operation in all internal nodes.",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{ODonnell:2015:HMM,
author = "Ryan O'Donnell and Yi Wu and Yuan Zhou",
title = "Hardness of {Max-2Lin} and {Max-3Lin} over Integers,
Reals, and Large Cyclic Groups",
journal = j-TOCT,
volume = "7",
number = "2",
pages = "9:1--9:??",
month = may,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2751322",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue May 12 06:02:22 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "In 1997, H{\aa}stad showed NP-hardness of $ (1 -
\epsilon, 1 / q + \delta)$-approximating Max-3Lin($
Z_q$); however, it was not until 2007 that Guruswami
and Raghavendra were able to show NP-hardness of $ (1 -
\epsilon, \delta)$-approximating Max-3Lin($Z$). In
2004, Khot--Kindler--Mossel--O'Donnell showed
UG-hardness of $ (1 - \epsilon, \delta)$-approximating
Max-2Lin($ Z_q$) for $ q = q (\epsilon, \delta)$ a
sufficiently large constant; however, achieving the
same hardness for Max-2Lin($Z$) was given as an open
problem in Raghavendra's 2009 thesis. In this work, we
show that fairly simple modifications to the proofs of
the Max-3Lin($ Z_q$) and Max-2Lin($ Z_q$) results yield
optimal hardness results over $Z$. In fact, we show a
kind of ``bicriteria'' hardness: Even when there is a $
(1 - \epsilon)$-good solution over $Z$, it is hard for
an algorithm to find a $ \delta $-good solution over
$Z$, $R$, or $ Z_m$ for any $ m \geq q (\epsilon,
\delta)$ of the algorithm's choosing.",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Ambainis:2015:LBD,
author = "Andris Ambainis and William Gasarch and Aravind
Srinivasan and Andrey Utis",
title = "Lower Bounds on the Deterministic and Quantum
Communication Complexity of {Hamming}-Distance
Problems",
journal = j-TOCT,
volume = "7",
number = "3",
pages = "10:1--10:??",
month = jul,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2698587",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Fri Aug 7 10:02:02 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Alice and Bob want to know if two strings of length n
are almost equal. That is, do the strings differ on at
most a bits? Let $ 0 \leq a \leq n - 1 $. We show (1)
any deterministic protocol-as well as any error-free
quantum protocol ($ C* $ version)-for this problem
requires at least $ n - 2 $ bits of communication, and
(2) a lower bound of $ n / 2 - 1 $ for error-free $ Q*
$ quantum protocols. We also show the same results for
determining if two strings differ in exactly $a$ bits.
Our results are obtained by lower-bounding the ranks of
the appropriate matrices.",
acknowledgement = ack-nhfb,
articleno = "10",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Jerrum:2015:SHF,
author = "Mark Jerrum and Kitty Meeks",
title = "Some Hard Families of Parameterized Counting
Problems",
journal = j-TOCT,
volume = "7",
number = "3",
pages = "11:1--11:??",
month = jul,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2786017",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Fri Aug 7 10:02:02 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We consider parameterized subgraph counting problems
of the following form: given a graph $f$G, how many
$k$-tuples of its vertices induce a subgraph with a
given property? A number of such problems are known to
be \#W[1]-complete; here, we substantially generalize
some of these existing results by proving hardness for
two large families of such problems. We demonstrate
that it is \#W[1]-hard to count the number of
$k$-vertex subgraphs having any property where the
number of distinct edge densities of labeled subgraphs
that satisfy the property is $ o(k^2)$. In the special
case in which the property in question depends only on
the number of edges in the subgraph, we give a
strengthening of this result, which leads to our second
family of hard problems.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Case:2015:MD,
author = "Adam Case and Jack H. Lutz",
title = "Mutual Dimension",
journal = j-TOCT,
volume = "7",
number = "3",
pages = "12:1--12:??",
month = jul,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2786566",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Fri Aug 7 10:02:02 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We define the lower and upper mutual dimensions $ {\rm
mdim}(x : y) $ and $ {\rm Mdim}(x : y) $ between any
two points $x$ and $y$ in Euclidean space. Intuitively,
these are the lower and upper densities of the
algorithmic information shared by $x$ and $y$. We show
that these quantities satisfy the main desiderata for a
satisfactory measure of mutual algorithmic information.
Our main theorem, the data processing inequality for
mutual dimension, says that if $ f : R^m > R^n$ is
computable and Lipschitz, then the inequalities $ {\rm
mdim}(f(x) : y) \leq {\rm mdim} (x : y)$ and $ {\rm
Mdim}(f(x) : y) \leq {\rm Mdim}(x : y)$ hold for all $
x \in R^m$ and $ y \in R^t$. We use this inequality and
related inequalities that we prove in like fashion to
establish conditions under which various classes of
computable functions on Euclidean space preserve or
otherwise transform mutual dimensions between points.",
acknowledgement = ack-nhfb,
articleno = "12",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Fernau:2015:UPT,
author = "Henning Fernau and Alejandro L{\'o}pez-Ortiz and
Jazm{\'\i}n Romero",
title = "Using Parametric Transformations Toward Polynomial
Kernels for Packing Problems Allowing Overlaps",
journal = j-TOCT,
volume = "7",
number = "3",
pages = "13:1--13:??",
month = jul,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2786015",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Fri Aug 7 10:02:02 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We consider the problem of discovering overlapping
communities in networks that we model as
generalizations of the Set and Graph Packing problems
with overlap. As usual for Set Packing problems, we
seek a collection $ S^' \subseteq S $ consisting of at
least $k$ sets subject to certain disjointness
restrictions. In the $r$-Set Packing with
$t$-Membership, each element of $U$ belongs to at most
$t$ sets of $ S^'$, while in $r$-Set Packing with
$t$-Overlap, each pair of sets in $ S^'$ overlaps in at
most $t$ elements. For both problems, each set of $S$
has at most $r$ elements. Similarly, both of our Graph
Packing problems seek a collection $K$ of at least $k$
subgraphs in a graph $G$, each isomorphic to a graph $
H \in H$. In $H$-Packing with $t$-Membership, each
vertex of $G$ belongs to at most $t$ subgraphs of $K$,
while in $H$-Packing with $t$-Overlap, each pair of
subgraphs in K overlaps in at most $t$ vertices. For
both problems, each member of $H$ has at most $r$
vertices and $m$ edges, where $t$, $r$, and $m$ are
constants. Here, we show NP-completeness results for
all of our packing problems. Furthermore, we give a
dichotomy result for the $H$-Packing with
$t$-Membership problem analogous to the Kirkpatrick and
Hell dichotomy [Kirkpatrick and Hell 1978]. Using
polynomial parameter transformations, we reduce the
$r$-Set Packing with $t$-Membership to a problem kernel
with $ O((r + 1)^r k^r)$ elements and the $H$ Packing
with $t$-Membership and its edge version to problem
kernels with $ O((r + 1)^r k^r)$ and $ O((m + 1)^m
k^m)$ vertices, respectively. On the other hand, by
generalizing [Fellows et al. 2008; Moser 2009], we
achieve a kernel with $ O(r^r k^{r - t - 1})$ elements
for the $r$-Set Packing with $t$ Overlap and kernels
with $ O(r^r k^{r - t - 1})$ and $ O(m^m k^{m - t -
1})$ vertices for the $H$-Packing with $t$-Overlap and
its edge version, respectively. In all cases, $k$ is
the input parameter, while $t$, $r$, and $m$ are
constants.",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Drange:2015:ESC,
author = "P{\aa}l Gr{\o}n{\aa}s Drange and Fedor V. Fomin and
Michal Pilipczuk and Yngve Villanger",
title = "Exploring the Subexponential Complexity of Completion
Problems",
journal = j-TOCT,
volume = "7",
number = "4",
pages = "14:1--14:??",
month = sep,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2799640",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Oct 1 16:40:05 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Let $F$ be a family of graphs. In the $F$-Completion
problem, we are given an $n$-vertex graph $G$ and an
integer $k$ as input, and asked whether at most $k$
edges can be added to $G$ so that the resulting graph
does not contain a graph from $F$ as an induced
subgraph. It was shown recently that two special cases
of $F$-Completion, namely, (i) the problem of
completing into a chordal graph known as Minimum
Fill-in (SIAM J. Comput. 2013), which corresponds to
the case of $ F = \{ C_4, C_5, C_6, \ldots \} $, and
(ii) the problem of completing into a split graph
(Algorithmica 2015), that is, the case of $ F = C_4, 2
K_2, C_5$, are solvable in parameterized subexponential
time $ 2^{O (\sqrt k \log k)} n^{O(1)}$. The
exploration of this phenomenon is the main motivation
for our research on $F$-Completion. In this article, we
prove that completions into several well-studied
classes of graphs without long induced cycles and paths
also admit parameterized subexponential time algorithms
by showing that: --- The problem Trivially Perfect
Completion, which is $F$-Completion for $ F = C_4,
P_4$, a cycle and a path on four vertices, is solvable
in parameterized subexponential time $ 2^{O (\sqrt k
\log k)} n^{O(1)}$. --- The problems known in the
literature as Pseudosplit Completion, the case in which
F2 $ K_2$, $ C_4$, and Threshold Completion, in which $
F = 2 K_2, P_4, C_4$, are also solvable in time $ 2^{O
(\sqrt k \log k)} n^{O(1)}$. We complement our
algorithms for $F$-Completion with the following lower
bounds: --- For $ F = 2 K_2$, $ F = C_4$,$ F = P o_4$,
and $ F = {2 K_2, P_4}$, $F$-Completion cannot be
solved in time $ 2^{o(k)} n^{O(1)}$ unless the
Exponential Time Hypothesis (ETH) fails. Our upper and
lower bounds provide a complete picture of the
subexponential parameterized complexity of
$F$-Completion problems for any $ F \subseteq {2 K_2,
C_4, P_4}$.",
acknowledgement = ack-nhfb,
articleno = "14",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Regev:2015:QXG,
author = "Oded Regev and Thomas Vidick",
title = "Quantum {XOR} Games",
journal = j-TOCT,
volume = "7",
number = "4",
pages = "15:1--15:??",
month = sep,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2799560",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Oct 1 16:40:05 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We introduce quantum XOR games, a model of two-player,
one-round games that extends the model of XOR games by
allowing the referee's questions to the players to be
quantum states. We give examples showing that quantum
XOR games exhibit a wide range of behaviors that are
known not to exist for standard XOR games, such as
cases in which the use of entanglement leads to an
arbitrarily large advantage over the use of no
entanglement. By invoking two deep extensions of
Grothendieck's inequality, we present an efficient
algorithm that gives a constant-factor approximation to
the best performance that players can obtain in a given
game, both in the case that they have no shared
entanglement and that they share unlimited
entanglement. As a byproduct of the algorithm, we prove
some additional interesting properties of quantum XOR
games, such as the fact that sharing a maximally
entangled state of arbitrary dimension gives only a
small advantage over having no entanglement at all.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Goldreich:2015:IOP,
author = "Oded Goldreich and Or Meir",
title = "Input-Oblivious Proof Systems and a Uniform Complexity
Perspective on {P\slash poly}",
journal = j-TOCT,
volume = "7",
number = "4",
pages = "16:1--16:??",
month = sep,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2799645",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Oct 1 16:40:05 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "An input-oblivious proof system is a proof system in
which the proof does not depend on the claim being
proved. Input-oblivious versions of NP and MA were
introduced in passing by Fortnow, Santhanam, and
Williams, who also showed that those classes are
related to questions on circuit complexity. In this
article, we wish to highlight the notion of
input-oblivious proof systems and initiate a more
systematic study of them. We begin by describing in
detail the results of Fortnow et al. and discussing
their connection to circuit complexity. We then extend
the study to input-oblivious versions of IP, and PCP,
and ZK and present few preliminary results regarding
those versions.",
acknowledgement = ack-nhfb,
articleno = "16",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Teutsch:2015:ADM,
author = "Jason Teutsch and Marius Zimand",
title = "On Approximate Decidability of Minimal Programs",
journal = j-TOCT,
volume = "7",
number = "4",
pages = "17:1--17:??",
month = sep,
year = "2015",
CODEN = "????",
DOI = "https://doi.org/10.1145/2799561",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Thu Oct 1 16:40:05 MDT 2015",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "An index $e$ in a numbering of partial-recursive
functions is called minimal if every lesser index
computes a different function from $e$. Since the
1960s, it has been known that, in any reasonable
programming language, no effective procedure determines
whether or not a given index is minimal. We investigate
whether the task of determining minimal indices can be
solved in an approximate sense. Our first question,
regarding the set of minimal indices, is whether there
exists an algorithm that can correctly label 1 out of
$k$ indices as either minimal or nonminimal. Our second
question, regarding the function that computes minimal
indices, is whether one can compute a short list of
candidate indices that includes a minimal index for a
given program. We give negative answers to both
questions for the important case of numberings with
linearly bounded translators.",
acknowledgement = ack-nhfb,
articleno = "17",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Kratsch:2016:PCK,
author = "Stefan Kratsch and D{\'a}niel Marx and Magnus
Wahlstr{\"o}m",
title = "Parameterized Complexity and Kernelizability of Max
Ones and Exact Ones Problems",
journal = j-TOCT,
volume = "8",
number = "1",
pages = "1:1--1:??",
month = feb,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2858787",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Sat Feb 6 08:06:18 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "For a finite set $ \Gamma $ of Boolean relations, Max
Ones SAT($ \Gamma $) and Exact Ones SAT($ \Gamma $) are
generalized satisfiability problems where every
constraint relation is from $ \Gamma $, and the task is
to find a satisfying assignment with at least/exactly
$k$ variables set to $1$, respectively. We study the
parameterized complexity of these problems, including
the question whether they admit polynomial kernels. For
Max Ones SAT($ \Gamma $), we give a classification into
five different complexity levels: polynomial-time
solvable, admits a polynomial kernel, fixed-parameter
tractable, solvable in polynomial time for fixed $k$,
and NP-hard already for $ k = 1$. For Exact Ones SAT($
\Gamma $), we refine the classification obtained
earlier by taking a closer look at the fixed-parameter
tractable cases and classifying the sets $ \Gamma $ for
which Exact Ones SAT($ \Gamma $) admits a polynomial
kernel.",
acknowledgement = ack-nhfb,
articleno = "1",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Volkovich:2016:CAR,
author = "Ilya Volkovich",
title = "Characterizing Arithmetic Read-Once Formulae",
journal = j-TOCT,
volume = "8",
number = "1",
pages = "2:1--2:??",
month = feb,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2858783",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Sat Feb 6 08:06:18 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "An arithmetic Read-Once Formula (ROF for short) is a
formula (i.e., a tree of computation) in which the
operations are $ \{ +, \times \} $ and such that every
input variable labels at most one leaf. We give a
simple characterization of such formulae. Other than
being interesting in its own right, our
characterization gives rise to a property-testing
algorithm for functions computable by such formulae. To
the best of our knowledge, prior to our work, no
characterization and/or property-testing algorithm was
known for this kind of formulae.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Schmitz:2016:CHB,
author = "Sylvain Schmitz",
title = "Complexity Hierarchies beyond Elementary",
journal = j-TOCT,
volume = "8",
number = "1",
pages = "3:1--3:??",
month = feb,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2858784",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Sat Feb 6 08:06:18 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We introduce a hierarchy of fast-growing complexity
classes and show its suitability for completeness
statements of many nonelementary problems. This
hierarchy allows the classification of many decision
problems with a nonelementary complexity, which occur
naturally in areas such as logic, combinatorics, formal
languages, and verification, with complexities ranging
from simple towers of exponentials to Ackermannian and
beyond.",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Ailon:2016:OLR,
author = "Nir Ailon",
title = "An {$ \Omega ((n \log n) / R) $} Lower Bound for
{Fourier} Transform Computation in the {$R$}-Well
Conditioned Model",
journal = j-TOCT,
volume = "8",
number = "1",
pages = "4:1--4:??",
month = feb,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2858785",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Sat Feb 6 08:06:18 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Obtaining a nontrivial (superlinear) lower bound for
computation of the Fourier transform in the linear
circuit model has been a long-standing open problem for
more than 40 years. An early result by Morgenstern from
1973, provides an $ \Omega (n \log n) $ lower bound for
the unnormalized Fourier transform when the constants
used in the computation are bounded. The proof uses a
potential function related to a determinant. That
result does not explain why the normalized Fourier
transform (of unit determinant) should be difficult to
compute in the same model. Hence, it is not scale
insensitive. More recently, Ailon [2013] showed that if
only unitary 2-by-2 gates are used, and additionally no
extra memory is allowed, then the normalized Fourier
transform requires $ \Omega (n \log n) $ steps. This
rather limited result is also sensitive to scaling, but
highlights the complexity inherent in the Fourier
transform arising from introducing entropy, unlike,
say, the identity matrix (which is as complex as the
Fourier transform using Morgenstern's arguments, under
proper scaling). This work improves on Ailon [2013] in
two ways: First, we eliminate the scaling restriction
and provide a lower bound for computing any scaling of
the Fourier transform. Second, we allow the
computational model to use extra memory. Our
restriction is that the composition of all gates up to
any point must be a well- conditioned linear
transformation. The lower bound is $ \Omega (R^{-1} n
\log n) $, where $R$ is the uniform condition number.
Well-conditioned is a natural requirement for
algorithms accurately computing linear transformations
on machine architectures of bounded word size. Hence,
this result can be seen as a tradeoff between speed and
accuracy. The main technical contribution is an
extension of matrix entropy used in Ailon [2013] for
unitary matrices to a potential function computable for
any invertible matrix, using ``quasi-entropy'' of
``quasi-probabilities.''",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Fischer:2016:TRO,
author = "Eldar Fischer and Yonatan Goldhirsh and Oded Lachish",
title = "Testing Read-Once Formula Satisfaction",
journal = j-TOCT,
volume = "8",
number = "2",
pages = "5:1--5:??",
month = may,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2897184",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Sat May 21 08:02:14 MDT 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We study the query complexity of testing for
properties defined by read-once formulas, as instances
of massively parametrized properties, and prove several
testability and nontestability results. First, we prove
the testability of any property accepted by a Boolean
read-once formula involving any bounded arity gates,
with a number of queries exponential in $ \epsilon $,
doubly exponential in the arity, and independent of all
other parameters. When the gates are limited to being
monotone, we prove that there is an estimation
algorithm that outputs an approximation of the distance
of the input from satisfying the property. For formulas
only involving And/Or gates, we provide a more
efficient test whose query complexity is only
quasipolynomial in $ \epsilon $ . On the other hand, we
show that such testability results do not hold in
general for formulas over non-Boolean alphabets.
Specifically, we construct a property defined by a
read-once arity 2 (non-Boolean) formula over an
alphabet of size 4, such that any 1/4-test for it
requires a number of queries depending on the formula
size. We also present such a formula over an alphabet
of size 5 that also satisfies a strong monotonicity
condition.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Fellows:2016:TPM,
author = "Michael R. Fellows and Danny Hermelin and Frances
Rosamond and Hadas Shachnai",
title = "Tractable Parameterizations for the Minimum Linear
Arrangement Problem",
journal = j-TOCT,
volume = "8",
number = "2",
pages = "6:1--6:??",
month = may,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2898352",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Sat May 21 08:02:14 MDT 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The M inimum Linear Arrangement (MLA) problem involves
embedding a given graph on the integer line so that the
sum of the edge lengths of the embedded graph is
minimized. Most layout problems are either intractable
or not known to be tractable, parameterized by the
treewidth of the input graph. We investigate MLA with
respect to three parameters that provide more structure
than treewidth. In particular, we give a factor $ (1 +
\epsilon) $-approximation algorithm for MLA
parameterized by $ (\epsilon, k) $, where $k$ is the
vertex cover number of the input graph. By a similar
approach, we obtain two FPT algorithms that exactly
solve MLA parameterized by, respectively, the max leaf
and edge clique cover numbers of the input graph.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Goldreich:2016:SBT,
author = "Oded Goldreich and Dana Ron",
title = "On Sample-Based Testers",
journal = j-TOCT,
volume = "8",
number = "2",
pages = "7:1--7:??",
month = may,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2898355",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Sat May 21 08:02:14 MDT 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The standard definition of property testing endows the
tester with the ability to make arbitrary queries to
``elements'' of the tested object. In contrast,
sample-based testers only obtain independently
distributed elements (a.k.a. labeled samples) of the
tested object. While sample-based testers were defined
by Goldreich, Goldwasser, and Ron (JACM 1998), with
few exceptions, most research in property testing has
focused on query-based testers. In this work, we
advance the study of sample-based property testers by
providing several general positive results as well as
by revealing relations between variants of this testing
model. In particular: -We show that certain types of
query-based testers yield sample-based testers of
sublinear sample complexity. For example, this holds
for a natural class of proximity oblivious testers. -We
study the relation between distribution-free
sample-based testers and one-sided error sample-based
testers w.r.t. the uniform distribution. While most of
this work ignores the time complexity of testing, one
part of it does focus on this aspect. The main result
in this part is a sublinear- time sample-based tester,
in the dense graphs model, for $k$-colorability, for any
$k \geq 2$.",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Kumar:2016:ACL,
author = "Mrinal Kumar and Gaurav Maheshwari and Jayalal Sarma",
title = "Arithmetic Circuit Lower Bounds via Maximum-Rank of
Partial Derivative Matrices",
journal = j-TOCT,
volume = "8",
number = "3",
pages = "8:1--8:??",
month = may,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2898437",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed May 25 17:15:05 MDT 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We introduce the polynomial coefficient matrix and
identify the maximum rank of this matrix under variable
substitution as a complexity measure for multivariate
polynomials. We use our techniques to prove
super-polynomial lower bounds against several classes
of non-multilinear arithmetic circuits. In particular,
we obtain the following results: --- As our first main
result, we prove that any homogeneous depth-3 circuit
for computing the product of d matrices of dimension $
n \times $ n requires $ \Omega (n^{d - 1} / 2^d) $
size. This improves the lower bounds in Nisan and
Wigderson [1995] for $ d = \omega (1) $. --- As our
second main result, we show that there is an explicit
polynomial on $n$ variables and degree at most $ n / 2$
for which any depth-$3$ circuit of product dimension at
most $ n / 10$ (dimension of the space of affine forms
feeding into each product gate) requires size $
2^{\Omega (n)}$. This generalizes the lower bounds
against diagonal circuits proved in Saxena [2008].
Diagonal circuits are of product dimension $1$. --- We
prove a $ n^{ \Omega ( = log n)}$ lower bound on the
size of product-sparse formulas. By definition, any
multilinear formula is a product-sparse formula. Thus,
this result extends the known super-polynomial lower
bounds on the size of multilinear formulas [Raz 2006].
--- We prove a $ 2^{ \Omega (n)}$ lower bound on the
size of partitioned arithmetic branching programs. This
result extends the known exponential lower bound on the
size of ordered arithmetic branching programs [Jansen
2008].",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Fulla:2016:GCW,
author = "Peter Fulla and Stanislav Zivn{\'y}",
title = "A {Galois} Connection for Weighted (Relational) Clones
of Infinite Size",
journal = j-TOCT,
volume = "8",
number = "3",
pages = "9:1--9:??",
month = may,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2898438",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed May 25 17:15:05 MDT 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "A Galois connection between clones and relational
clones on a fixed finite domain is one of the
cornerstones of the so-called algebraic approach to the
computational complexity of non-uniform Constraint
Satisfaction Problems (CSPs). Cohen et al. established
a Galois connection between finitely-generated weighted
clones and finitely-generated weighted relational
clones [SICOMP'13], and asked whether this connection
holds in general. We answer this question in the
affirmative for weighted (relational) clones with real
weights and show that the complexity of the
corresponding valued CSPs is preserved.",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Haviv:2016:LDS,
author = "Ishay Haviv and Oded Regev",
title = "The List-Decoding Size of {Fourier}-Sparse {Boolean}
Functions",
journal = j-TOCT,
volume = "8",
number = "3",
pages = "10:1--10:??",
month = may,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2898439",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed May 25 17:15:05 MDT 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "A function defined on the Boolean hypercube is
$k$-Fourier-sparse if it has at most $k$ nonzero
Fourier coefficients. For a function $ f : F_2^n \to R$
and parameters $k$ and $d$, we prove a strong upper
bound on the number of $k$-Fourier-sparse Boolean
functions that disagree with $f$ on at most $d$ inputs.
Our bound implies that the number of uniform and
independent random samples needed for learning the
class of $k$-Fourier-sparse Boolean functions on $n$
variables exactly is at most $ O (n \cdot k \log k)$.
As an application, we prove an upper bound on the query
complexity of testing Booleanity of Fourier-sparse
functions. Our bound is tight up to a logarithmic
factor and quadratically improves on a result due to
Gur and Tamuz [2013].",
acknowledgement = ack-nhfb,
articleno = "10",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Nguyen:2016:SPN,
author = "Dung Nguyen and Alan L. Selman",
title = "Structural Properties of Nonautoreducible Sets",
journal = j-TOCT,
volume = "8",
number = "3",
pages = "11:1--11:??",
month = may,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2898440",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed May 25 17:15:05 MDT 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We investigate autoreducibility properties of complete
sets for NEXP under different polynomial-time
reductions. Specifically, we show under some
polynomial-time reductions that there are complete sets
for NEXP that are not autoreducible. We obtain the
following main results: -For any positive integers s
and k such that 2$^s$ --- 1 {$>$} k, there is a
\leq $_{s - T}^p$ -complete set for NEXP that is not
\leq $_{k - tt}^p$ -autoreducible. -For every constant
c {$>$} 1, there is a \leq $_{2 - T}^p$ -complete set
for NEXP that is not autoreducible under nonadaptive
reductions that make no more than three queries, such
that each of them has a length between n$^{1 / c}$ and
n$^c$, where n is input size. -For any positive integer
k, there is a \leq $_{k - tt}^p$ -complete set for
NEXP that is not autoreducible under \leq $_{k -
tt}^p$ -reductions whose truth table is not a
disjunction or a negated disjunction. Finally, we show
that settling the question of whether every
\leq $_{dtt}^p$ -complete set for NEXP is \leq $_{NOR
- tt}^p$ -autoreducible either positively or negatively
would lead to major results about the exponential time
complexity classes.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Gobel:2016:CHS,
author = "Andreas G{\"o}bel and Leslie Ann Goldberg and David
Richerby",
title = "Counting Homomorphisms to Square-Free Graphs, Modulo
2",
journal = j-TOCT,
volume = "8",
number = "3",
pages = "12:1--12:??",
month = may,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2898441",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed May 25 17:15:05 MDT 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We study the problem $ \oplus $ Homs ToH of counting,
modulo 2, the homomorphisms from an input graph to a
fixed undirected graph H. A characteristic feature of
modular counting is that cancellations make wider
classes of instances tractable than is the case for
exact (nonmodular) counting; thus, subtle dichotomy
theorems can arise. We show the following dichotomy:
for any $H$ that contains no 4-cycles, $ \oplus $ Homs
To H is either in polynomial time or is $ \oplus $
P-complete. This partially confirms a conjecture of
Faben and Jerrum that was previously only known to hold
for trees and for a restricted class of tree-width-2
graphs called cactus graphs. We confirm the conjecture
for a rich class of graphs, including graphs of
unbounded tree-width. In particular, we focus on
square-free graphs, which are graphs without 4-cycles.
These graphs arise frequently in combinatorics, for
example, in connection with the strong perfect graph
theorem and in certain graph algorithms. Previous
dichotomy theorems required the graph to be tree-like
so that tree-like decompositions could be exploited in
the proof. We prove the conjecture for a much richer
class of graphs by adopting a much more general
approach.",
acknowledgement = ack-nhfb,
articleno = "12",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Caragiannis:2016:LDA,
author = "Ioannis Caragiannis and Christos Kaklamanis and Maria
Kyropoulou",
title = "Limitations of Deterministic Auction Design for
Correlated Bidders",
journal = j-TOCT,
volume = "8",
number = "4",
pages = "13:1--13:??",
month = jul,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2934309",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Dec 26 17:25:10 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The seminal work of Myerson (Mathematics of OR '81)
characterizes incentive-compatible single-item auctions
among bidders with independent valuations. In this
setting, relatively simple deterministic auction
mechanisms achieve revenue optimality. When bidders
have correlated valuations, designing the
revenue-optimal deterministic auction is a
computationally demanding problem; indeed,
Papadimitriou and Pierrakos (STOC '11) proved that it
is APX-hard, obtaining an explicit inapproximability
factor of 1999/2000 = 99.95\%. In the current article,
we strengthen this inapproximability factor to 63/64
\approx 98.5\%. Our proof is based on a gap-preserving
reduction from the M ax-NM 3SAT problem; a variant of
the maximum satisfiability problem where each clause
has exactly three literals and no clause contains both
negated and unnegated literals. We furthermore show
that the gap between the revenue of deterministic and
randomized auctions can be as low as 13/14 \approx
92.9\%, improving an explicit gap of 947/948 \approx
99.9\% by Dobzinski, Fu, and Kleinberg (STOC '11).",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Gurjar:2016:PGP,
author = "Rohit Gurjar and Arpita Korwar and Jochen Messner and
Simon Straub and Thomas Thierauf",
title = "Planarizing Gadgets for Perfect Matching Do Not
Exist",
journal = j-TOCT,
volume = "8",
number = "4",
pages = "14:1--14:??",
month = jul,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2934310",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Dec 26 17:25:10 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "To reduce a graph problem to its planar version, a
standard technique is to replace crossings in a drawing
of the input graph by planarizing gadgets. We show
unconditionally that such a reduction is not possible
for the perfect matching problem and also extend this
to some other problems related to perfect matching. We
further show that there is no planarizing gadget for
the Hamiltonian cycle problem.",
acknowledgement = ack-nhfb,
articleno = "14",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Ron:2016:PEH,
author = "Dana Ron and Gilad Tsur",
title = "The Power of an Example: Hidden Set Size Approximation
Using Group Queries and Conditional Sampling",
journal = j-TOCT,
volume = "8",
number = "4",
pages = "15:1--15:??",
month = jul,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2930657",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Dec 26 17:25:10 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We study a basic problem of approximating the size of
an unknown set S in a known universe U. We consider two
versions of the problem. In both versions, the
algorithm can specify subsets T \subseteq U. In the
first version, which we refer to as the group query or
subset query version, the algorithm is told whether T
\cap S is nonempty. In the second version, which we
refer to as the subset sampling version, if T \cap S is
nonempty, then the algorithm receives a uniformly
selected element from T \cap S. We study the difference
between these two versions in both the case that the
algorithm is adaptive and the case in which it is
nonadaptive. Our main focus is on a natural family of
allowed subsets, which correspond to intervals, as well
as variants of this family.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Gal:2016:SEA,
author = "Anna G{\'a}l and Jing-Tang Jang and Nutan Limaye and
Meena Mahajan and Karteek Sreenivasaiah",
title = "Space-Efficient Approximations for Subset Sum",
journal = j-TOCT,
volume = "8",
number = "4",
pages = "16:1--16:??",
month = jul,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2894843",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Dec 26 17:25:10 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "SubsetSum is a well-known NP-complete problem: given
$t \in Z^+$ and a set $S$ of $m$ positive integers,
output YES if and only if there is a subset $S'
\subseteq S$ such that the sum of all numbers in $S'$
equals $t$. The problem and its search and optimization
versions are known to be solvable in pseudopolynomial
time in general. We develop a one-pass deterministic
streaming algorithm that uses space $ O(\frac {\log
t}{\epsilon })$ and decides if some subset of the input
stream adds up to a value in the range $ \{ (1 \pm
\epsilon) t \} $. Using this algorithm, we design
space-efficient fully polynomial-time approximation
schemes (FPTAS) solving the search and optimization
versions of SubsetSum. Our algorithms run in $ O(\frac
{1}{\epsilon m^2})$ time and $ O(\frac {1}{\epsilon })$
space on unit-cost RAMs, where $ 1 + \epsilon $ is the
approximation factor. This implies constant space
quadratic time FPTAS on unit-cost RAMs when \epsilon is
a constant. Previous FPTAS used space linear in $m$. In
addition, we show that on certain inputs, when a
solution is located within a short prefix of the input
sequence, our algorithms may run in sublinear time. We
apply our techniques to the problem of finding balanced
separators, and we extend our results to some other
variants of the more general knapsack problem. When the
input numbers are encoded in unary, the decision
version has been known to be in $ \log $ space. We give
streaming space lower and upper bounds for unary
SubsetSum (USS). If the input length is $N$ when the
numbers are encoded in unary, we show that randomized s
pass streaming algorithms for exact SubsetSum need
space $ \Omega (\frac {\sqrt {N}}{s})$ and give a
simple deterministic two-pass streaming algorithm using
$ O(\sqrt {N \log N})$ space. Finally, we formulate an
encoding under which USS is monotone and show that the
exact and approximate versions in this formulation have
monotone $ O(\log^2 t)$ depth Boolean circuits. We also
show that any circuit using $ \epsilon $-approximator
gates for SubsetSum under this encoding needs $ \Omega
(n / \log n)$ gates to compute the disjointness
function.",
acknowledgement = ack-nhfb,
articleno = "16",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Lauria:2016:RLB,
author = "Massimo Lauria",
title = "A Rank Lower Bound for Cutting Planes Proofs of
{Ramsey's Theorem}",
journal = j-TOCT,
volume = "8",
number = "4",
pages = "17:1--17:??",
month = jul,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2903266",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Dec 26 17:25:10 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Ramsey's Theorem is a cornerstone of combinatorics and
logic. In its simplest formulation it says that for
every $ k > 0 $ and $ s > 0 $, there is a minimum
number $ r(k, s) $ such that any simple graph with at
least $ r (k, s) $ vertices contains either a clique of
size $k$ or an independent set of size $s$. We study
the complexity of proving upper bounds for the number $
r (k, k)$. In particular, we focus on the propositional
proof system cutting planes; we show that any cutting
plane proof of the upper bound ``$ r (k, k) \leq 4^k$''
requires high rank. In order to do that we show a
protection lemma which could be of independent
interest.",
acknowledgement = ack-nhfb,
articleno = "17",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Viola:2016:QMH,
author = "Emanuele Viola",
title = "Quadratic Maps Are Hard to Sample",
journal = j-TOCT,
volume = "8",
number = "4",
pages = "18:1--18:??",
month = jul,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2934308",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Dec 26 17:25:10 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "This note proves the existence of a quadratic GF(2)
map $ p \colon \{ 0, 1 \}^n \to \{ 0, 1 \} $ such that
no constant-depth circuit of size $ \poly (n) $ can
sample the distribution $ (u, p(u)) $ for uniform
$u$.",
acknowledgement = ack-nhfb,
articleno = "18",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Hrubes:2016:HMV,
author = "P. Hrubes",
title = "On Hardness of Multilinearization and
{VNP}-Completeness in Characteristic $2$",
journal = j-TOCT,
volume = "9",
number = "1",
pages = "1:1--1:??",
month = dec,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2940323",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Dec 26 17:25:10 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "For a Boolean function $ f \colon \{ 0, 1 \}^n \to \{
0, 1 \} $, let $ \fcirc $ be the unique multilinear
polynomial such that $ f(x) = \fcirc (x) $ holds for
every $ x \in \{ 0, 1 \}^n $. We show that, assuming VP
/= VNP, there exists a polynomial-time computable $f$
such that $ \fcirc $ requires superpolynomial
arithmetic circuits. In fact, this $f$ can be taken as
a monotone 2-CNF, or a product of affine functions.
This holds over any field. To prove the results in
characteristic 2, we design new VNP-complete families
in this characteristic. This includes the polynomial
EC$_n$ counting edge covers in a graph and the
polynomial mclique$_n$ counting cliques in a graph with
deleted perfect matching. They both correspond to
polynomial-time decidable problems, a phenomenon
previously encountered only in characteristic /= 2.",
acknowledgement = ack-nhfb,
articleno = "1",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Krebs:2016:SDP,
author = "Andreas Krebs and Nutan Limaye and Meena Mahajan and
Karteek Sreenivasaiah",
title = "Small Depth Proof Systems",
journal = j-TOCT,
volume = "9",
number = "1",
pages = "2:1--2:??",
month = dec,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2956229",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Dec 26 17:25:10 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "A proof system for a language L is a function f such
that Range( f ) is exactly L. In this article, we look
at proof systems from a circuit complexity point of
view and study proof systems that are computationally
very restricted. The restriction we study is proof
systems that can be computed by bounded fanin circuits
of constant depth (NC$^0$ ) or of O (log \log n ) depth
but with O (1) alternations (poly \log AC$^0$ ). Each
output bit depends on very few input bits; thus such
proof systems correspond to a kind of local error
correction on a theorem-proof pair. We identify exactly
how much power we need for proof systems to capture all
regular languages. We show that all regular languages
have poly \log AC$^0$ proof systems, and from a
previous result (Beyersdorff et al. [2011a], where
NC$^0$ proof systems were first introduced), this is
tight. Our technique also shows that M aj has poly \log
AC$^0$ proof system. We explore the question of whether
T aut has NC$^0$ proof systems. Addressing this
question about 2TAUT, and since 2TAUT is closely
related to reachability in graphs, we ask the same
question about Reachability. We show that if Directed
reachability has NC$^0$ proof systems, then so does
2TAUT. We then show that both Undirected Reachability
and Directed UnReachability have NC$^0$ proof systems,
but Directed Reachability is still open. In the context
of how much power is needed for proof systems for
languages in NP, we observe that proof systems for a
good fraction of languages in NP do not need the full
power of AC$^0$; they have SAC$^0$ or coSAC$^0$ proof
systems.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Arvind:2016:NVC,
author = "V. Arvind and P. S. Joglekar and S. Raja",
title = "Noncommutative {Valiant}'s Classes: Structure and
Complete Problems",
journal = j-TOCT,
volume = "9",
number = "1",
pages = "3:1--3:??",
month = dec,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2956230",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Dec 26 17:25:10 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "In this article, we explore the noncommutative
analogues, VP$_{nc}$ and VNP$_{nc}$, of Valiant's
algebraic complexity classes and show some striking
connections to classical formal language theory. Our
main results are the following: --- We show that Dyck
polynomials (defined from the Dyck languages of formal
language theory) are complete for the class VP$_{nc}$
under $ \leq_{abp}$ reductions. To the best of our
knowledge, these are the first natural polynomial
families shown to be VP$_{nc}$ -complete. Likewise, it
turns out that PAL (palindrome polynomials defined from
palindromes) are complete for the class VSKEW$_{nc}$
(defined by polynomial-size skew circuits) under $
\leq_{abp}$ reductions. The proof of these results is
by suitably adapting the classical
Chomsky--Sch{\"u}tzenberger theorem showing that Dyck
languages are the hardest CFLs. --- Assuming that
VP$_{nc}$ /= VNP$_{nc}$, we exhibit a strictly infinite
hierarchy of $p$-families, with respect to the
projection reducibility, between the complexity classes
VP$_{nc}$ and VNP$_{nc}$ (analogous to Ladner's theorem
[Ladner 1975]). --- Additionally, inside VP$_{nc}$, we
show that there is a strict hierarchy of p-families
(based on the nesting depth of Dyck polynomials) with
respect to the $ \leq_{abp}$ reducibility (defined
explicitly in this article).",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Fontes:2016:RDD,
author = "Lila Fontes and Rahul Jain and Iordanis Kerenidis and
Sophie Laplante and Mathieu Lauri{\`e}re and
J{\'e}r{\'e}mie Roland",
title = "Relative Discrepancy Does Not Separate Information and
Communication Complexity",
journal = j-TOCT,
volume = "9",
number = "1",
pages = "4:1--4:??",
month = dec,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/2967605",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Dec 26 17:25:10 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Does the information complexity of a function equal
its communication complexity? We examine whether any
currently known techniques might be used to show a
separation between the two notions. Ganor et al. [2014]
recently provided such a separation in the
distributional case for a specific input distribution.
We show that in the non-distributional setting, the
relative discrepancy bound is smaller than the
information complexity; hence, it cannot separate
information and communication complexity. In addition,
in the distributional case, we provide a linear program
formulation for relative discrepancy and relate it to
variants of the partition bound, resolving also an open
question regarding the relation of the partition bound
and information complexity. Last, we prove the
equivalence between the adaptive relative discrepancy
and the public-coin partition, implying that the
logarithm of the adaptive relative discrepancy bound is
quadratically tight with respect to communication.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Beame:2016:NAF,
author = "Paul Beame and Nathan Grosshans and Pierre McKenzie
and Luc Segoufin",
title = "Nondeterminism and An Abstract Formulation of
{Neciporuk}'s Lower Bound Method",
journal = j-TOCT,
volume = "9",
number = "1",
pages = "5:1--5:??",
month = dec,
year = "2016",
CODEN = "????",
DOI = "https://doi.org/10.1145/3013516",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Dec 26 17:25:10 MST 2016",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "A formulation of Neciporuk's lower bound method
slightly more inclusive than the usual
complexity-measure-specific formulation is
presented. Using this general formulation, limitations
to lower bounds achievable by the method are obtained
for several computation models, such as branching
programs and Boolean formulas having access to a
sublinear number of nondeterministic bits. In
particular, it is shown that any lower bound achievable
by the method of Neciporuk for the size of
nondeterministic and parity branching programs is at
most $O(n^{3 / 2} / \log n)$.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Artemenko:2017:PGO,
author = "Sergei Artemenko and Ronen Shaltiel",
title = "Pseudorandom Generators with Optimal Seed Length for
Non-{Boolean} Poly-Size Circuits",
journal = j-TOCT,
volume = "9",
number = "2",
pages = "6:1--6:??",
month = may,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3018057",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jul 24 17:35:50 MDT 2017",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "A sampling procedure for a distribution $P$ over $ \{
0, 1 \}^l$ is a function $ C : \{ 0, 1 \}^n \to \{ 0, 1
\}^l$ such that the distribution $ C(U_n)$ (obtained by
applying $C$ on the uniform distribution $ U_n$) is the
``desired distribution'' $P$. Let $ n > r \geq l =
n^{\Omega (1)}$. An $ \epsilon - n b$-PRG (defined by
Dubrov and Ishai [2006]) is a function $ G : \{ 0, 1
\}^r \to \{ 0, 1 \}^n$ such that for every $ C : \{ 0,
1 \}^n \to \{ 0, 1 \}^l$ in some class of ``interesting
sampling procedures,'' '$ C(U_r) = C(G (U_r))$ is $
\epsilon $-close to $ C(U_n)$ in statistical distance.
We construct poly-time computable nb-PRGs with $ r = O
(l)$ for poly-size circuits relying on the assumption
that there exists $ \beta > 0$ and a problem $L$ in $ E
= {\rm DTIME}(2^{O(n)})$ such that for every large
enough n, nondeterministic circuits of size $ 2^{ \beta
n}$ that have NP-gates cannot solve $L$ on inputs of
length $n$. This assumption is a scaled nonuniform
analog of (the widely believed) EXP /= $ \Sigma_2^P$,
and similar assumptions appear in various contexts in
derandomization. Previous nb-PRGs of Dubrov and Ishai
have $ r = \Omega (l^2)$ and are based on very strong
cryptographic assumptions or, alternatively, on
nonstandard assumptions regarding incompressibility of
functions on random inputs. When restricting to
poly-size circuits $ C : \{ 0, 1 \}^n \to \{ 0, 1 \}^l$
with Shannon entropy $ H(C(U_n)) \leq k$, for $ l > k =
n^{\Omega (1)}$, our nb-PRGs have $ r = O (k)$. The
nb-PRGs of Dubrov and Ishai use seed length $ r =
\Omega (k^2)$ and require that the probability
distribution of $ C(U_n)$ is efficiently computable.
Our nb-PRGs follow from a notion of ``conditional
PRGs,'' which may be of independent interest. These are
PRGs where $ G(U_r)$ remains pseudorandom even when
conditioned on a ``large'' event $ \{ A(G(U_r)) = 1 \}
$, for an arbitrary poly-size circuit $A$. A related
notion was considered by Shaltiel and Umans [2005] in a
different setting, and our proofs use ideas from that
paper, as well as ideas of Dubrov and Ishai. We also
give an unconditional construction of poly-time
computable nb-PRGs for $ \poly (n)$-size, depth $d$
circuits $ C : \{ 0, 1 \}^n \to \{ 0, 1 \}^l$ with $ r
= O(l \cdot \log^{d + O (1)} n)$. This improves upon
the previous work of Dubrov and Ishai that has $ r \geq
l^2$. This result follows by adapting a recent PRG
construction of Trevisan and Xue [2013] to the case of
nb-PRGs. We also show that this PRG can be implemented
by a uniform family of constant-depth circuits with
slightly increased seed length.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Bhattacharyya:2017:LBC,
author = "Arnab Bhattacharyya and Sivakanth Gopi",
title = "Lower Bounds for Constant Query Affine-Invariant
{LCCs} and {LTCs}",
journal = j-TOCT,
volume = "9",
number = "2",
pages = "7:1--7:??",
month = may,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3016802",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jul 24 17:35:50 MDT 2017",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Affine-invariant codes are codes whose coordinates
form a vector space over a finite field and which are
invariant under affine transformations of the
coordinate space. They form a natural, well-studied
class of codes; they include popular codes such as
Reed--Muller and Reed--Solomon. A particularly
appealing feature of affine-invariant codes is that
they seem well suited to admit local correctors and
testers. In this work, we give lower bounds on the
length of locally correctable and locally testable
affine-invariant codes with constant query complexity.
We show that if a code $ C \subset \Sigma^{K n} $ is an
$r$-query affine invariant locally correctable code
(LCC), where $K$ is a finite field and $ \Sigma $ is a
finite alphabet, then the number of codewords in $C$ is
at most $ \exp (O_{K, r, | \Sigma |}(n^{r - 1}))$.
Also, we show that if $ C \subset \Sigma^K n$ is an
$r$-query affine invariant locally testable code (LTC),
then the number of codewords in C is at most $ \exp
(O_{K, r, | \Sigma |} (n^{r - 2}))$. The dependence on
n in these bounds is tight for constant-query
LCCs/LTCs, since Guo, Kopparty, and Sudan (ITCS'13)
constructed affine-invariant codes via lifting that
have the same asymptotic tradeoffs. Note that our
result holds for non-linear codes, whereas previously,
Ben-Sasson and Sudan (RANDOM'11) assumed linearity to
derive similar results. Our analysis uses higher-order
Fourier analysis. In particular, we show that the
codewords corresponding to an affine-invariant LCC/LTC
must be far from each other with respect to Gowers norm
of an appropriate order. This then allows us to bound
the number of codewords, using known decomposition
theorems, which approximate any bounded function in
terms of a finite number of low-degree non-classical
polynomials, up to a small error in the Gowers norm.",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Gurjar:2017:EPM,
author = "Rohit Gurjar and Arpita Korwar and Jochen Messner and
Thomas Thierauf",
title = "Exact Perfect Matching in Complete Graphs",
journal = j-TOCT,
volume = "9",
number = "2",
pages = "8:1--8:??",
month = may,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3041402",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jul 24 17:35:50 MDT 2017",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "A red-blue graph is a graph where every edge is
colored either red or blue. The exact perfect matching
problem asks for a perfect matching in a red-blue graph
that has exactly a given number of red edges. We show
that for complete and bipartite complete graphs, the
exact perfect matching problem is logspace equivalent
to the perfect matching problem. Hence, an efficient
parallel algorithm for perfect matching would carry
over to the exact perfect matching problem for this
class of graphs. We also report some progress in
extending the result to arbitrary graphs.",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Galanis:2017:CTA,
author = "Andreas Galanis and Leslie Ann Goldberg and Mark
Jerrum",
title = "A Complexity Trichotomy for Approximately Counting
List {$H$}-Colorings",
journal = j-TOCT,
volume = "9",
number = "2",
pages = "9:1--9:??",
month = may,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3037381",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jul 24 17:35:50 MDT 2017",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We examine the computational complexity of
approximately counting the list H -colorings of a
graph. We discover a natural graph-theoretic trichotomy
based on the structure of the graph H. If H is an
irreflexive bipartite graph or a reflexive complete
graph, then counting list H -colorings is trivially in
polynomial time. Otherwise, if H is an irreflexive
bipartite permutation graph or a reflexive proper
interval graph, then approximately counting list H
-colorings is equivalent to \#BIS, the problem of
approximately counting independent sets in a bipartite
graph. This is a well-studied problem that is believed
to be of intermediate complexity-it is believed that it
does not have an FPRAS, but that it is not as difficult
as approximating the most difficult counting problems
in \#P. For every other graph H, approximately counting
list H -colorings is complete for \#P with respect to
approximation-preserving reductions (so there is no
FPRAS unless NP = RP). Two pleasing features of the
trichotomy are (1) it has a natural formulation in
terms of hereditary graph classes, and (2) the proof is
largely self-contained and does not require any
universal algebra (unlike similar dichotomies in the
weighted case). We are able to extend the hardness
results to the bounded-degree setting, showing that all
hardness results apply to input graphs with maximum
degree at most 6.",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Dhayal:2017:MMP,
author = "Anant Dhayal and Jayalal Sarma and Saurabh Sawlani",
title = "Min\slash Max-Poly Weighting Schemes and the {NL}
versus {UL} Problem",
journal = j-TOCT,
volume = "9",
number = "2",
pages = "10:1--10:??",
month = may,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3070902",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jul 24 17:35:50 MDT 2017",
bibsource = "http://www.acm.org/pubs/contents/journals/toct/;
http://www.math.utah.edu/pub/tex/bib/hash.bib;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "For a graph $ G (V, E) (| V | = n) $ and a vertex $ s
\in V $, a weighting scheme $ (W : E \mapsto Z^+) $ is
called a min-unique (resp. max-unique) weighting scheme
if, for any vertex $v$ of the graph $G$, there is a
unique path of minimum (resp. maximum) weight from $s$
to $v$, where weight of a path is the sum of the
weights assigned to the edges. Instead, if the number
of paths of minimum (resp. maximum) weight is bounded
by $ n^c$ for some constant $c$, then the weighting
scheme is called a min-poly (resp. max-poly) weighting
scheme. In this article, we propose an unambiguous
nondeterministic log-space (UL) algorithm for the
problem of testing reachability graphs augmented with a
min-poly weighting scheme. This improves the result in
Reinhardt and Allender [2000], in which a UL algorithm
was given for the case when the weighting scheme is
min-unique. Our main technique involves triple
inductive counting and generalizes the techniques of
Immerman [1988], Szelepcs{\'e}nyi [1988], and Reinhardt
and Allender [2000], combined with a hashing technique
due to Fredman et al. [1984] (also used in Garvin et
al. [2014]). We combine this with a complementary
unambiguous verification method to give the desired UL
algorithm. At the other end of the spectrum, we propose
a UL algorithm for testing reachability in layered DAGs
augmented with max-poly weighting schemes. To achieve
this, we first reduce reachability in layered DAGs to
the longest path problem for DAGs with a unique source,
such that the reduction also preserves the max-unique
and max-poly properties of the graph. Using our
techniques, we generalize the double inductive counting
method in Limaye et al. [2009], in which the UL
algorithm was given for the longest path problem on
DAGs with a unique sink and augmented with a max-unique
weighting scheme. An important consequence of our
results is that, to show NL = UL, it suffices to design
log-space computable min-poly (or max-poly) weighting
schemes for layered DAGs.",
acknowledgement = ack-nhfb,
articleno = "10",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Chen:2017:AMC,
author = "Hubie Chen and Benoit Larose",
title = "Asking the Metaquestions in Constraint Tractability",
journal = j-TOCT,
volume = "9",
number = "3",
pages = "11:1--11:??",
month = oct,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3134757",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jan 22 09:30:15 MST 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The constraint satisfaction problem (CSP) involves
deciding, given a set of variables and a set of
constraints on the variables, whether or not there is
an assignment to the variables satisfying all of the
constraints. One formulation of the CSP is as the
problem of deciding, given a pair (G H) of relational
structures, whether or not there is a homomorphism from
the first structure to the second structure. The CSP is
generally NP-hard; a common way to restrict this
problem is to fix the second structure H so that each
structure H gives rise to a problem CSP(H). The problem
family CSP(H) has been studied using an algebraic
approach, which links the algorithmic and complexity
properties of each problem CSP(H) to a set of
operations, the so-called polymorphisms of H. Certain
types of polymorphisms are known to imply the
polynomial-time tractability of CSP(H), and others are
conjectured to do so. This article systematically
studies-for various classes of polymorphisms-the
computational complexity of deciding whether or not a
given structure H admits a polymorphism from the class.
Among other results, we prove the NP-completeness of
deciding a condition conjectured to characterize the
tractable problems CSP(H), as well as the
NP-completeness of deciding if CSP(H) has bounded
width.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Elberfeld:2017:CGB,
author = "Michael Elberfeld and Pascal Schweitzer",
title = "Canonizing Graphs of Bounded Tree Width in Logspace",
journal = j-TOCT,
volume = "9",
number = "3",
pages = "12:1--12:??",
month = oct,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3132720",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jan 22 09:30:15 MST 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Graph canonization is the problem of computing a
unique representative, a canon, from the isomorphism
class of a given graph. This implies that two graphs
are isomorphic exactly if their canons are equal. We
show that graphs of bounded tree width can be canonized
by logarithmic-space (logspace) algorithms. This
implies that the isomorphism problem for graphs of
bounded tree width can be decided in logspace. In the
light of isomorphism for trees being hard for the
complexity class logspace, this makes the ubiquitous
class of graphs of bounded tree width one of the few
classes of graphs for which the complexity of the
isomorphism problem has been exactly determined.",
acknowledgement = ack-nhfb,
articleno = "12",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Schmid:2017:FCS,
author = "Markus L. Schmid",
title = "Finding Consensus Strings with Small Length Difference
between Input and Solution Strings",
journal = j-TOCT,
volume = "9",
number = "3",
pages = "13:1--13:??",
month = oct,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3110290",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jan 22 09:30:15 MST 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The Closest Substring Problem is to decide, for given
strings $ s_1 $, \ldots{}, $ s_k $ of length at most
$l$ and numbers $m$ and $d$, whether there is a
length-$m$ string $s$ and length-$m$ substrings $
s^'_i$ of s$_i$, such that $s$ has a Hamming distance
of at most $d$ from each $ s^'_i$. If we instead
require the sum of all the Hamming distances between
$s$ and each $ s^'_i$ to be bounded by $d$, then it is
called the Consensus Patterns Problem. We contribute to
the parameterised complexity analysis of these
classical NP-hard string problems by investigating the
parameter ($ l - m$), i.e., the length difference
between input and solution strings. For most
combinations of ($ l - m$) and one of the classical
parameters ($m$, $l$, $k$, or $d$), we obtain
fixed-parameter tractability. However, even for
constant ($ l - m$) and constant alphabet size, both
problems remain NP-hard. While this follows from known
results with respect to the Closest Substring, we need
a new reduction in the case of the Consensus Patterns.
As a by-product of this reduction, we obtain an exact
exponential-time algorithm for both problems, which is
based on an alphabet reduction.",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Adamaszek:2017:HAS,
author = "Anna Adamaszek and Tomasz Kociumaka and Marcin
Pilipczuk and Michal Pilipczuk",
title = "Hardness of Approximation for Strip Packing",
journal = j-TOCT,
volume = "9",
number = "3",
pages = "14:1--14:??",
month = oct,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3092026",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jan 22 09:30:15 MST 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Strip packing is a classical packing problem, where
the goal is to pack a set of rectangular objects into a
strip of a given width, while minimizing the total
height of the packing. The problem has multiple
applications, for example, in scheduling and
stock-cutting, and has been studied extensively. When
the dimensions of the objects are allowed to be
exponential in the total input size, it is known that
the problem cannot be approximated within a factor
better than 3/2, unless P = NP. However, there was no
corresponding lower bound for polynomially bounded
input data. In fact, Nadiradze and Wiese [SODA 2016]
have recently proposed a $ (1.4 +
\epsilon)$-approximation algorithm for this variant,
thus showing that strip packing with polynomially
bounded data can be approximated better than when
exponentially large values are allowed in the input.
Their result has subsequently been improved to a $ (4 /
3 + \epsilon)$-approximation by two independent
research groups [FSTTCS 2016, WALCOM 2017]. This raises
a question whether strip packing with polynomially
bounded input data admits a quasi-polynomial time
approximation scheme, as is the case for related
two-dimensional packing problems like maximum
independent set of rectangles or two-dimensional
knapsack. In this article, we answer this question in
negative by proving that it is NP-hard to approximate
strip packing within a factor better than 12/11, even
when restricted to polynomially bounded input data. In
particular, this shows that the strip packing problem
admits no quasi-polynomial time approximation scheme,
unless NP $ \subseteq $ DTIME($ 2^{\polylog (n)}$).",
acknowledgement = ack-nhfb,
articleno = "14",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Chen:2017:PCM,
author = "Hubie Chen",
title = "Proof Complexity Modulo the Polynomial Hierarchy:
Understanding Alternation as a Source of Hardness",
journal = j-TOCT,
volume = "9",
number = "3",
pages = "15:1--15:??",
month = oct,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3087534",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jan 22 09:30:15 MST 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We present and study a framework in which one can
present alternation-based lower bounds on proof length
in proof systems for quantified Boolean formulas. A key
notion in this framework is that of proof system
ensemble, which is (essentially) a sequence of proof
systems where, for each, proof checking can be
performed in the polynomial hierarchy. We introduce a
proof system ensemble called relaxing QU-res that is
based on the established proof system QU-resolution.
Our main results include an exponential separation of
the treelike and general versions of relaxing QU-res
and an exponential lower bound for relaxing QU-res;
these are analogs of classical results in propositional
proof complexity.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Iwama:2018:PT,
author = "Kazuo Iwama and Yuichi Yoshida",
title = "Parameterized Testability",
journal = j-TOCT,
volume = "9",
number = "4",
pages = "16:1--16:??",
month = jan,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3155294",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jan 22 09:30:15 MST 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "This article studies property testing for NP
optimization problems with parameter $k$ under the
general graph model with an augmentation of random edge
sampling capability. It is shown that a variety of such
problems, including $k$-Vertex Cover, $k$-Feedback
Vertex Set, $k$-Multicut, $k$-Path-Free, and
$k$-Dominating Set, are constant-query testable if $k$
is constant. It should be noted that the first four
problems are fixed parameter tractable (FPT) and it
turns out that algorithmic techniques for their FPT
algorithms (branch-and-bound search, color coding,
etc.) are also useful for our testers. $k$-Dominating
Set is $ W [2]$-hard, but we can still test the
property with a constant number of queries, since the
definition of $ \epsilon $-farness makes the problem
trivial for non-sparse graphs that are the source of
hardness for the original optimization problem. We also
consider $k$-Odd Cycle Transversal, which is another
well-known FPT problem, but we only give a
sublinear-query tester when $k$ is a constant.",
acknowledgement = ack-nhfb,
articleno = "16",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Pallavoor:2018:PPT,
author = "Ramesh Krishnan S. Pallavoor and Sofya Raskhodnikova
and Nithin Varma",
title = "Parameterized Property Testing of Functions",
journal = j-TOCT,
volume = "9",
number = "4",
pages = "17:1--17:??",
month = jan,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3155296",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jan 22 09:30:15 MST 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We investigate the parameters in terms of which the
complexity of sublinear-time algorithms should be
expressed. Our goal is to find input parameters that
are tailored to the combinatorics of the specific
problem being studied and design algorithms that run
faster when these parameters are small. This direction
enables us to surpass the (worst-case) lower bounds,
expressed in terms of the input size, for several
problems. Our aim is to develop a similar level of
understanding of the complexity of sublinear-time
algorithms to the one that was enabled by research in
parameterized complexity for classical algorithms.
Specifically, we focus on testing properties of
functions. By parameterizing the query complexity in
terms of the size r of the image of the input function,
we obtain testers for monotonicity and convexity of
functions of the form $ f \colon [n] \to R $ with query
complexity $ O(\log r) $, with no dependence on $n$.
The result for monotonicity circumvents the $ \Omega
(\log n)$ lower bound by Fischer (Inf. Comput. 2004)
for this problem. We present several other
parameterized testers, providing compelling evidence
that expressing the query complexity of property
testers in terms of the input size is not always the
best choice.",
acknowledgement = ack-nhfb,
articleno = "17",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Pilipczuk:2018:SEA,
author = "Michal Pilipczuk and Marcin Wrochna",
title = "On Space Efficiency of Algorithms Working on
Structural Decompositions of Graphs",
journal = j-TOCT,
volume = "9",
number = "4",
pages = "18:1--18:??",
month = jan,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3154856",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jan 22 09:30:15 MST 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Dynamic programming on path and tree decompositions of
graphs is a technique that is ubiquitous in the field
of parameterized and exponential-time algorithms.
However, one of its drawbacks is that the space usage
is exponential in the decomposition's width. Following
the work of Allender et al. [5], we investigate whether
this space complexity explosion is unavoidable. Using
the idea of reparameterization of Cai and Juedes [18],
we prove that the question is closely related to a
conjecture that the Longest Common Subsequence problem
parameterized by the number of input strings does not
admit an algorithm that simultaneously uses XP time and
FPT space. Moreover, we extend the complexity landscape
sketched for pathwidth and treewidth by Allender et al.
by considering the parameter tree-depth. We prove that
computations on tree-depth decompositions correspond to
a model of non-deterministic machines that work in
polynomial time and logarithmic space, with access to
an auxiliary stack of maximum height equal to the
decomposition's depth. Together with the results of
Allender et al., this describes a hierarchy of
complexity classes for polynomial-time
non-deterministic machines with different restrictions
on the access to working space, which mirrors the
classic relations between treewidth, pathwidth, and
tree-depth.",
acknowledgement = ack-nhfb,
articleno = "18",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Chakraborty:2018:SPT,
author = "Diptarka Chakraborty and Raghunath Tewari",
title = "An {$ O(n \epsilon) $} Space and Polynomial Time
Algorithm for Reachability in Directed Layered Planar
Graphs",
journal = j-TOCT,
volume = "9",
number = "4",
pages = "19:1--19:??",
month = jan,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3154857",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jan 22 09:30:15 MST 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Given a graph $G$ and two vertices $s$ and $t$ in it,
graph reachability is the problem of checking whether
there exists a path from $s$ to $t$ in $G$. We show
that reachability in directed layered planar graphs can
be decided in polynomial time and $ O(n^\epsilon)$
space, for any $ \epsilon > 0$. The previous best-known
space bound for this problem with polynomial time was
approximately $ O(\sqrt n)$ space (Imai et al. 2013).
Deciding graph reachability in SC (Steve's class) is an
important open question in complexity theory, and in
this article, we make progress toward resolving this
question.",
acknowledgement = ack-nhfb,
articleno = "19",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Chang:2018:MMS,
author = "Ching-Lueh Chang",
title = "Metric $1$-Median Selection: Query Complexity vs.
Approximation Ratio",
journal = j-TOCT,
volume = "9",
number = "4",
pages = "20:1--20:??",
month = jan,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3154858",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Mon Jan 22 09:30:15 MST 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Consider the problem of finding a point in a metric
space $ (\{ 1, 2, \ldots, n \}, d) $ with the minimum
average distance to other points. We show that this
problem has no deterministic $ o(n^{1 + 1 / (h - 1)} /
h)$-query $ 2 h c (1 - \epsilon)$-approximation
algorithms for any constant $ \epsilon > 0$ and any $ h
= h (n) \in Z^+ \backslash \{ 1 \} $ satisfying $ h = o
(n 1 / (h - 1))$. Combining our result with existing
ones, we determine the best approximation ratio
achievable by deterministic $ O(n^{1 + \epsilon
})$-query (respectively, $ O(n^{1 + \epsilon })$-time)
algorithms to be $ 2 \lceil 1 / \epsilon \rceil $, for
all constants $ \epsilon \in (0, 1)$.",
acknowledgement = ack-nhfb,
articleno = "20",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Aydinlioglu:2018:ARU,
author = "Baris Aydinlioglu and Eric Bach",
title = "Affine Relativization: Unifying the Algebrization and
Relativization Barriers",
journal = j-TOCT,
volume = "10",
number = "1",
pages = "1:1--1:??",
month = jan,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3170704",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:49 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We strengthen existing evidence for the so-called
``algebrization barrier.'' Algebrization-short for
algebraic relativization-was introduced by Aaronson and
Wigderson (AW) (STOC 2008) to characterize proofs
involving arithmetization, simulation, and other
``current techniques.'' However, unlike relativization,
eligible statements under this notion do not seem to
have basic closure properties, making it conceivable to
take two proofs, both with algebrizing conclusions, and
combine them to get a proof without. Further, the
notion is undefined for most types of statements and
does not seem to yield a general criterion by which we
can tell, given a proof, whether it algebrizes. In
fact, the very notion of an algebrizing proof is never
made explicit, and casual attempts to define it are
problematic. All these issues raise the question of
what evidence, if any, is obtained by knowing whether
some statement does or does not algebrize. We give a
reformulation of algebrization without these
shortcomings. First, we define what it means for any
statement/proof to hold relative to any language, with
no need to refer to devices like a Turing machine with
an oracle tape. Our approach dispels the widespread
misconception that the notion of oracle access is
inherently tied to a computational model. We also
connect relativizing statements to proofs, by showing
that every proof that some statement relativizes is
essentially a relativizing proof of that statement. We
then define a statement/proof as relativizing affinely
if it holds relative to every affine oracle -here an
affine oracle is the result of a particular error
correcting code applied to the characteristic string of
a language. We show that every statement that AW
declare as algebrizing does relativize affinely, in
fact, has a proof that relativizes affinely, and that
no such proof exists for any of the statements shown
not-algebrizing by AW in the classical computation
model. Our work complements, and goes beyond, the
subsequent work by Impagliazzo, Kabanets, and
Kolokolova (STOC 2009), which also proposes a
reformulation of algebrization, but falls short of
recovering some key results of AW, most notably
regarding the NEXP versus P/poly question. Using our
definitions, we obtain new streamlined proofs of
several classic results in complexity, including PSPACE
\subset IP and NEXP \subset MIP. This may be of
separate interest.",
acknowledgement = ack-nhfb,
articleno = "1",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Watson:2018:CCS,
author = "Thomas Watson",
title = "Communication Complexity of Statistical Distance",
journal = j-TOCT,
volume = "10",
number = "1",
pages = "2:1--2:??",
month = jan,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3170708",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:49 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We prove nearly matching upper and lower bounds on the
randomized communication complexity of the following
problem: Alice and Bob are each given a probability
distribution over n elements, and they wish to estimate
within \pm \epsilon the statistical (total variation)
distance between their distributions. For some range of
parameters, there is up to a log n factor gap between
the upper and lower bounds, and we identify a barrier
to using information complexity techniques to improve
the lower bound in this case. We also prove a side
result that we discovered along the way: the randomized
communication complexity of n -bit Majority composed
with n -bit Greater Than is \Theta ( n log n ).",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Anderson:2018:ITL,
author = "Matthew Anderson and Michael A. Forbes and Ramprasad
Saptharishi and Amir Shpilka and Ben Lee Volk",
title = "Identity Testing and Lower Bounds for Read-$k$
Oblivious Algebraic Branching Programs",
journal = j-TOCT,
volume = "10",
number = "1",
pages = "3:1--3:??",
month = jan,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3170709",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:49 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Read-$k$ oblivious algebraic branching programs are a
natural generalization of the well-studied model of
read-once oblivious algebraic branching program (ABP).
In this work, we give an exponential lower bound of $
\exp (n / k^{O(k)})$ on the width of any read-$k$
oblivious ABP computing some explicit multilinear
polynomial $f$ that is computed by a polynomial-size
depth-3 circuit. We also study the polynomial identity
testing (PIT) problem for this model and obtain a
white-box subexponential-time PIT algorithm. The
algorithm runs in time $ 2^{\~ O(n^{1 - 1 / (2k) -
1})}$ and needs white box access only to know the order
in which the variables appear in the ABP.",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Goos:2018:RCV,
author = "Mika G{\"o}{\"o}s and T. S. Jayram and Toniann Pitassi
and Thomas Watson",
title = "Randomized Communication versus Partition Number",
journal = j-TOCT,
volume = "10",
number = "1",
pages = "4:1--4:??",
month = jan,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3170711",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:49 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We show that randomized communication complexity can
be superlogarithmic in the partition number of the
associated communication matrix, and we obtain
near-optimal randomized lower bounds for the Clique
versus Independent Set problem. These results
strengthen the deterministic lower bounds obtained in
prior work (G{\"o}{\"o}s, Pitassi, and Watson,
FOCS'15). One of our main technical contributions
states that information complexity when the cost is
measured with respect to only 1-inputs (or only
0-inputs) is essentially equivalent to information
complexity with respect to all inputs.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{ODonnell:2018:WCQ,
author = "Ryan O'Donnell and A. C. Cem Say",
title = "The Weakness of {CTC} Qubits and the Power of
Approximate Counting",
journal = j-TOCT,
volume = "10",
number = "2",
pages = "5:1--5:??",
month = may,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3196832",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We present results in structural complexity theory
concerned with the following interrelated topics:
computation with postselection/restarting, closed
timelike curves (CTCs), and approximate counting. The
first result is a new characterization of the lesser
known complexity class BPP$_{path}$ in terms of more
familiar concepts. Precisely, BPP$_{path}$ is the class
of problems that can be efficiently solved with a
nonadaptive oracle for the approximate counting
problem. Similarly, PP equals the class of problems
that can be solved efficiently with nonadaptive queries
for the related approximate difference problem. Another
result is concerned with the computational power
conferred by CTCs, or equivalently, the computational
complexity of finding stationary distributions for
quantum channels. Using the preceding characterization
of PP, we show that any poly( n )-time quantum
computation using a CTC of O (log n ) qubits may as
well just use a CTC of 1 classical bit. This result
essentially amounts to showing that one can find a
stationary distribution for a poly( n )-dimensional
quantum channel in PP.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Komusiewicz:2018:TRT,
author = "Christian Komusiewicz",
title = "Tight Running Time Lower Bounds for Vertex Deletion
Problems",
journal = j-TOCT,
volume = "10",
number = "2",
pages = "6:1--6:??",
month = may,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3186589",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "For a graph class $ \Pi $, the $ \Pi $-Vertex Deletion
problem has as input an undirected graph G = ( V, E )
and an integer k and asks whether there is a set of at
most k vertices that can be deleted from G such that
the resulting graph is a member of $ \Pi $. By a
classic result of Lewis and Yannakakis [17], $ \Pi
$-Vertex Deletion is NP-hard for all hereditary
properties $ \Pi $. We adapt the original NP-hardness
construction to show that under the exponential time
hypothesis (ETH), tight complexity results can be
obtained. We show that \Pi -Vertex Deletion does not
admit a 2$^{o (n)}$ -time algorithm where n is the
number of vertices in G. We also obtain a dichotomy for
running time bounds that include the number m of edges
in the input graph. On the one hand, if $ \Pi $
contains all edgeless graphs, then there is no 2$^{o (n
+ m)}$ -time algorithm for \Pi -Vertex Deletion. On the
other hand, if there is a fixed edgeless graph that is
not contained in $ \Pi $ and containment in $ \Pi $ can
be determined in 2$^{O (n)}$ time or 2$^{o (m)}$ time,
then $ \Pi $-Vertex Deletion can be solved in 2$^{O (\&
sqrt; m)}$ + O ( n ) or 2$^{o (m)}$ + O ( n ) time,
respectively. We also consider restrictions on the
domain of the input graph G. For example, we obtain
that $ \Pi $-Vertex Deletion cannot be solved in 2$^{o
(\& sqrt; n)}$ time if G is planar and $ \Pi $ is
hereditary and contains and excludes infinitely many
planar graphs. Finally, we provide similar results for
the problem variant where the deleted vertex set has to
induce a connected graph.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Lutz:2018:AIP,
author = "Jack H. Lutz and Neil Lutz",
title = "Algorithmic Information, Plane {Kakeya} Sets, and
Conditional Dimension",
journal = j-TOCT,
volume = "10",
number = "2",
pages = "7:1--7:??",
month = may,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3201783",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We formulate the conditional Kolmogorov complexity of
x given y at precision r, where x and y are points in
Euclidean spaces and r is a natural number. We
demonstrate the utility of this notion in two ways; (1)
We prove a point-to-set principle that enables one to
use the (relativized, constructive) dimension of a
single point in a set E in a Euclidean space to
establish a lower bound on the (classical) Hausdorff
dimension of E. We then use this principle, together
with conditional Kolmogorov complexity in Euclidean
spaces, to give a new proof of the known,
two-dimensional case of the Kakeya conjecture. This
theorem of geometric measure theory, proved by Davies
in 1971, says that every plane set containing a unit
line segment in every direction has Hausdorff dimension
2. (2)We use conditional Kolmogorov complexity in
Euclidean spaces to develop the lower and upper
conditional dimensions dim( x | y ) and Dim( x | y ) of
x given y, where x and y are points in Euclidean
spaces. Intuitively, these are the lower and upper
asymptotic algorithmic information densities of x
conditioned on the information in y. We prove that
these conditional dimensions are robust and that they
have the correct information-theoretic relationships
with the well-studied dimensions dim( x ) and Dim( x )
and the mutual dimensions mdim( x: y ) and Mdim( x: y
).",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Gharibian:2018:GSC,
author = "Sevag Gharibian and Jamie Sikora",
title = "Ground State Connectivity of Local {Hamiltonians}",
journal = j-TOCT,
volume = "10",
number = "2",
pages = "8:1--8:??",
month = may,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3186587",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The study of ground state energies of local
Hamiltonians has played a fundamental role in quantum
complexity theory. In this article, we take a new
direction by introducing the physically motivated
notion of ``ground state connectivity'' of local
Hamiltonians, which captures problems in areas ranging
from quantum stabilizer codes to quantum memories.
Roughly, ``ground state connectivity'' corresponds to
the natural question: Given two ground states | \Psi
\rangle and | \phi \rangle of a local Hamiltonian H, is
there an ``energy barrier'' (with respect to H ) along
any sequence of local operations mapping | \Psi \rangle
to | \phi \rangle ? We show that the complexity of this
question can range from QCMA-complete to
PSPACE-complete, as well as NEXP-complete for an
appropriately defined ``succinct'' version of the
problem. As a result, we obtain a natural QCMA-complete
problem, a goal which has generally proven difficult
since the conception of QCMA over a decade ago. Our
proofs rely on a new technical tool, the Traversal
Lemma, which analyzes the Hilbert space a local unitary
evolution must traverse under certain conditions. We
show that this lemma is essentially tight with respect
to the length of the unitary evolution in question.",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Bliznets:2018:HAF,
author = "Ivan Bliznets and Marek Cygan and Pawel Komosa and
Michal Pilipczuk",
title = "Hardness of Approximation for {$H$}-free Edge
Modification Problems",
journal = j-TOCT,
volume = "10",
number = "2",
pages = "9:1--9:??",
month = may,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3196834",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The H --- free Edge Deletion problem asks, for a given
graph G and integer k, whether it is possible to delete
at most k edges from G to make it H -free-that is, not
containing H as an induced subgraph. The H -free Edge
Completion problem is defined similarly, but we add
edges instead of deleting them. The study of these two
problem families has recently been the subject of
intensive studies from the point of view of
parameterized complexity and kernelization. In
particular, it was shown that the problems do not admit
polynomial kernels (under plausible complexity
assumptions) for almost all graphs H, with several
important exceptions occurring when the class of H
-free graphs exhibits some structural properties. In
this work, we complement the parameterized study of
edge modification problems to H -free graphs by
considering their approximability. We prove that
whenever H is 3-connected and has at least two
nonedges, then both H --- free Edge Deletion and H
-free Edge Completion are very hard to approximate:
they do not admit poly(OPT)-approximation in polynomial
time, unless P=NP, or even in time subexponential in
OPT, unless the exponential time hypothesis fails. The
assumption of the existence of two nonedges appears to
be important: we show that whenever H is a complete
graph without one edge, then H -free Edge Deletion is
tightly connected to the Min Horn Deletion problem,
whose approximability is still open. Finally, in an
attempt to extend our hardness results beyond
3-connected graphs, we consider the cases of H being a
path or a cycle, and we achieve an almost complete
dichotomy there.",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Minahan:2018:CDI,
author = "Daniel Minahan and Ilya Volkovich",
title = "Complete Derandomization of Identity Testing and
Reconstruction of Read-Once Formulas",
journal = j-TOCT,
volume = "10",
number = "3",
pages = "10:1--10:??",
month = jun,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3196836",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "In this article, we study the identity testing problem
of arithmetic read-once formulas (ROFs) and some
related models. An ROF is a formula (a circuit whose
underlying graph is a tree) in which the operations are
{ +, $ \times $ } and such that every input variable
labels at most one leaf. We obtain the first
polynomial-time deterministic identity testing
algorithm that operates in the black-box setting for
ROFs, as well as some other related models. As an
application, we obtain the first polynomial-time
deterministic reconstruction algorithm for such
formulas. Our results are obtained by improving and
extending the analysis of the algorithm of Shpilka and
Yolkovich [51].",
acknowledgement = ack-nhfb,
articleno = "10",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Filmus:2018:IPS,
author = "Yuval Filmus and Guy Kindler and Elchanan Mossel and
Karl Wimmer",
title = "Invariance Principle on the Slice",
journal = j-TOCT,
volume = "10",
number = "3",
pages = "11:1--11:??",
month = jun,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3186590",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The non-linear invariance principle of Mossel,
O'Donnell, and Oleszkiewicz establishes that if $
f(x_1, \ldots, x_n) $ is a multilinear low-degree
polynomial with low influences, then the distribution
of if $ f(b_1, \ldots, b_n) $ is close (in various
senses) to the distribution of $ f(G_1, \ldots, G_n) $,
where $ B_i \in R \{ - 1, 1 \} $ are independent
Bernoulli random variables and $ G_i \asymp N(0, 1) $
are independent standard Gaussians. The invariance
principle has seen many applications in theoretical
computer science, including the Majority is Stablest
conjecture, which shows that the Goemans--Williamson
algorithm for MAX-CUT is optimal under the Unique Games
Conjecture. More generally, MOO's invariance principle
works for any two vectors of hypercontractive random
variables $ (X_1, \ldots, X_n) $, $ (Y_1, \ldots, Y_n)
$ such that (i) Matching moments: $ X_i $ and $ Y_i $
have matching first and second moments and (ii)
Independence: the variables $ X_1 $, \ldots, $ X_n $
are independent, as are $ Y_1 $, \ldots, $ Y_n $. The
independence condition is crucial to the proof of the
theorem, yet in some cases we would like to use
distributions $ X_1 $, \ldots, $ X_n $ in which the
individual coordinates are not independent. A common
example is the uniform distribution on the slice $
(^{[n]}_k) $ which consists of all vectors $ (x_1,
\ldots, x_n) \in \{ 0, 1 \}^n $ with Hamming weight
$k$. The slice shows up in theoretical computer science
(hardness amplification, direct sum testing), extremal
combinatorics (Erd{\H{o}}s--Ko--Rado theorems), and
coding theory (in the guise of the Johnson association
scheme). Our main result is an invariance principle in
which $ (X_1, \ldots, X_n)$ is the uniform distribution
on a slice $ (^{[n]}_{pn})$ and $ (Y_1, \ldots, Y_n)$
consists either of $n$ independent $ {\em Ber}(p)$
random variables, or of $n$ independent $ N(p, p (1 -
p))$ random variables. As applications, we prove a
version of Majority is Stablest for functions on the
slice, a version of Bourgain's tail theorem, a version
of the Kindler-Safra structural theorem, and a
stability version of the $t$-intersecting
Erd{\H{o}}s--Ko--Rado theorem, combining techniques of
Wilson and Friedgut. Our proof relies on a combination
of ideas from analysis and probability, algebra, and
combinatorics. In particular, we make essential use of
recent work of the first author which describes an
explicit Fourier basis for the slice.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Thapper:2018:LSR,
author = "Johan Thapper and Stanislav Zivn{\'y}",
title = "The Limits of {SDP} Relaxations for General-Valued
{CSPs}",
journal = j-TOCT,
volume = "10",
number = "3",
pages = "12:1--12:??",
month = jun,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3201777",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "It has been shown that for a general-valued constraint
language \Gamma the following statements are
equivalent: (1) any instance of VCSP( \Gamma ) can be
solved to optimality using a constant level of the
Sherali--Adams LP hierarchy, (2) any instance of VCSP(
\Gamma ) can be solved to optimality using the third
level of the Sherali--Adams LP hierarchy, and (3) the
support of \Gamma satisfies the `` bounded width
condition '' (i.e., it contains weak near-unanimity
operations of all arities). We show that if the support
of \Gamma violates the bounded width condition then not
only is VCSP( \Gamma ) not solved by a constant level
of the Sherali--Adams LP hierarchy, but it also
requires linear levels of the Lasserre SDP hierarchy
(also known as the sum-of-squares SDP hierarchy). For
\Gamma corresponding to linear equations in an Abelian
group, this result follows from existing work on
inapproximability of Max-CSPs. By a breakthrough result
of Lee, Raghavendra, and Steurer [STOC'15], our result
implies that for any \Gamma whose support violates the
bounded width condition no SDP relaxation of polynomial
size solves VCSP( \Gamma ). We establish our result by
proving that various reductions preserve exact
solvability by the Lasserre SDP hierarchy (up to a
constant factor in the level of the hierarchy). Our
results hold for general-valued constraint languages
(i.e., sets of functions on a fixed finite domain that
take on rational or infinite values) and thus also hold
in notable special cases of { 0, \infty }-valued
languages (CSPs), {0, 1}-valued languages
(Min-CSPs/Max-CSPs), and Q-valued languages
(finite-valued CSPs).",
acknowledgement = ack-nhfb,
articleno = "12",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Pilipczuk:2018:DMW,
author = "Marcin Pilipczuk and Magnus Wahlstr{\"o}m",
title = "Directed Multicut is {$ W[1] $}-hard, Even for Four
Terminal Pairs",
journal = j-TOCT,
volume = "10",
number = "3",
pages = "13:1--13:??",
month = jun,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3201775",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We prove that Multicut in directed graphs,
parameterized by the size of the cutset, is W [1]-hard
and hence unlikely to be fixed-parameter tractable even
if restricted to instances with only four terminal
pairs. This negative result almost completely resolves
one of the central open problems in the area of
parameterized complexity of graph separation problems,
posted originally by Marx and Razgon [SIAM J. Comput.
43(2):355--388 (2014)], leaving only the case of three
terminal pairs open. The case of two terminal pairs was
shown to be FPT by Chitnis et al. [SIAM J. Comput.
42(4):1674--1696 (2013)]. Our gadget methodology also
allows us to prove W [1]-hardness of the Steiner
Orientation problem parameterized by the number of
terminal pairs, resolving an open problem of Cygan,
Kortsarz, and Nutov [SIAM J. Discrete Math.
27(3):1503-1513 (2013)].",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Lee:2018:CPP,
author = "Chin Ho Lee and Emanuele Viola",
title = "The Coin Problem for Product Tests",
journal = j-TOCT,
volume = "10",
number = "3",
pages = "14:1--14:??",
month = jun,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3201787",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "Let X$_{m, \epsilon }$ be the distribution over m bits
X$_1$, \ldots{}, X$_m$ where the X$_i$ are independent
and each X$_i$ equals 1 with probability (1- \epsilon
)/2 and 0 with probability (1 --- \epsilon )/2. We
consider the smallest value \epsilon $^*$ of \epsilon
such that the distributions X$_{m, \epsilon }$ and
X$_{m, 0}$ can be distinguished with constant advantage
by a function f: {0,1}$^m$ -{$>$} S, which is the
product of k functions f$_1$, f$_2$, \ldots{}, f$_k$ on
disjoint inputs of n bits, where each f$_i$: {0,1}$^n$
-{$>$} S and m = nk. We prove that \epsilon $^*$ =
\Theta (1/\&sqrt; n log k ) if S = [-1,1], while
\epsilon $^*$ = \Theta (1/\&sqrt; nk ) if S is the set
of unit-norm complex numbers.",
acknowledgement = ack-nhfb,
articleno = "14",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Ganardi:2018:CEF,
author = "Moses Ganardi and Danny Hucke and Daniel K{\"o}nig and
Markus Lohrey",
title = "Circuits and Expressions over Finite Semirings",
journal = j-TOCT,
volume = "10",
number = "4",
pages = "15:1--15:??",
month = oct,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3241375",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "The computational complexity of the circuit and
expression evaluation problem for finite semirings is
considered, where semirings are not assumed to have an
additive or a multiplicative identity. The following
dichotomy is shown: If a finite semiring is such that
(i) the multiplicative semigroup is solvable and (ii)
it does not contain a subsemiring with an additive
identity 0 and a multiplicative identity 1 /= 0, then
the circuit evaluation problem is in DET \subseteq
NC$^2$, and the expression evaluation problem for the
semiring is in TC$^0$. For all other finite semirings,
the circuit evaluation problem is P-complete and the
expression evaluation problem is NC$^1$ -complete. As
an application, we determine the complexity of
intersection non-emptiness problems for given
context-free grammars (regular expressions) with a
fixed regular language.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Bhattacharyya:2018:PTJ,
author = "Rishiraj Bhattacharyya and Sourav Chakraborty",
title = "Property Testing of Joint Distributions using
Conditional Samples",
journal = j-TOCT,
volume = "10",
number = "4",
pages = "16:1--16:??",
month = oct,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3241377",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "In this article, we consider the problem of testing
properties of joint distributions under the Conditional
Sampling framework. In the standard sampling model,
sample complexity of testing properties of joint
distributions are exponential in the dimension,
resulting in inefficient algorithms for practical use.
While recent results achieve efficient algorithms for
product distributions with significantly smaller sample
complexity, no efficient algorithm is expected when the
marginals are not independent. In this article, we
initialize the study of conditional sampling in the
multidimensional setting. We propose a subcube
conditional sampling model where the tester can
condition on a (adaptively) chosen subcube of the
domain. Due to its simplicity, this model is
potentially implementable in many practical
applications, particularly when the distribution is a
joint distribution over \Sigma $^n$ for some set \Sigma
. We present algorithms for various fundamental
properties of distributions in the subcube-conditioning
model and prove that the sample complexity is
polynomial in the dimension n (and not exponential as
in the traditional model). We present an algorithm for
testing identity to a known distribution using {\~O}(
n$^2$ )-subcube-conditional samples, an algorithm for
testing identity between two unknown distributions
using {\~O}( n$^5$ )-subcube-conditional samples and an
algorithm for testing identity to a product
distribution using {\~O}( n$^5$ )-subcube-conditional
samples. The central concept of our technique involves
an elegant chain rule, which can be proved using basic
techniques of probability theory, yet it is powerful
enough to avoid the curse of dimensionality.",
acknowledgement = ack-nhfb,
articleno = "16",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Guo:2018:USM,
author = "Heng Guo and Pinyan Lu",
title = "Uniqueness, Spatial Mixing, and Approximation for
Ferromagnetic $2$-Spin Systems",
journal = j-TOCT,
volume = "10",
number = "4",
pages = "17:1--17:??",
month = oct,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3265025",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We give fully polynomial-time approximation schemes
(FPTAS) for the partition function of ferromagnetic
2-spin systems in certain parameter regimes. The
threshold we obtain is almost tight up to an
integrality gap. Our technique is based on the
correlation decay framework. The main technical
contribution is a new potential function, with which we
establish a new kind of spatial mixing.",
acknowledgement = ack-nhfb,
articleno = "17",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Agrawal:2018:SFV,
author = "Akanksha Agrawal and Daniel Lokshtanov and Amer E.
Mouawad and Saket Saurabh",
title = "Simultaneous Feedback Vertex Set: a Parameterized
Perspective",
journal = j-TOCT,
volume = "10",
number = "4",
pages = "18:1--18:??",
month = oct,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3265027",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "For a family F of graphs, a graph G, and a positive
integer k, the F-Deletion problem asks whether we can
delete at most k vertices from G to obtain a graph in
F. F-Deletion generalizes many classical graph problems
such as Vertex Cover, Feedback Vertex Set, and Odd
Cycle Transversal. For an integer $ \alpha \geq 1 $, an
$n$ vertex (multi) graph $ G = (V, \cup_{i = 1}^{
\alpha } E_i)$, where the edge set of $G$ is
partitioned into $ \alpha $ color classes, is called an
$ \alpha $-edge-colored (multi) graph. A natural
extension of the F-Deletion problem to edge-colored
graphs is the Simultaneous F Deletion problem. In the
latter problem, we are given an $ \alpha $-edge-colored
graph G and the goal is to find a set S of at most k
vertices such that each graph G$_i$ --- S, where G$_i$
= ( V, E$_i$ ) and $ 1 \leq i \leq \alpha $, is in F.
In this work, we study Simultaneous F-Deletion for F
being the family of forests. In other words, we focus
on the Simultaneous Feedback Vertex Set (SimFVS)
problem. Algorithmically, we show that, like its
classical counterpart, SimFVS parameterized by k is
fixed-parameter tractable (FPT) and admits a polynomial
kernel, for any fixed constant $ \alpha $. In
particular, we give an algorithm running in 2$^{O
(\alpha k)}$ n$^{O (1)}$ time and a kernel with O (
\alpha k$^{3(\alpha + 1)}$ ) vertices. The running time
of our algorithm implies that SimFVS is FPT even when $
\alpha \in o (\log n)$. We complement this positive
result by showing that if we allow $ \alpha $ to be in
$ O(\log n)$, where $n$ is the number of vertices in
the input graph, then SimFVS becomes $ W[1]$-hard. In
particular, when $ \alpha $ is roughly equal to $ c
\log n$, for a non-zero positive constant $c$, the
problem becomes $ W[1]$-hard. Our positive results
answer one of the open problems posed by Cai and Ye
(MFCS 2014).",
acknowledgement = ack-nhfb,
articleno = "18",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Boczkowski:2018:SCP,
author = "Lucas Boczkowski and Iordanis Kerenidis and
Fr{\'e}d{\'e}ric Magniez",
title = "Streaming Communication Protocols",
journal = j-TOCT,
volume = "10",
number = "4",
pages = "19:1--19:??",
month = oct,
year = "2018",
CODEN = "????",
DOI = "https://doi.org/10.1145/3276748",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Oct 17 17:24:50 MDT 2018",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
abstract = "We define the Streaming Communication model that
combines the main aspects of communication complexity
and streaming. Input arrives as a stream, spread
between several agents across a network. Each agent has
a bounded memory, which can be updated upon receiving a
new bit, or a message from another agent. We provide
tight tradeoffs between the necessary resources, i.e.,
communication between agents and memory, for some of
the canonical problems from communication complexity by
proving a strong general lower bound technique. Second,
we analyze the Approximate Matching problem and show
that the complexity of this problem (i.e., the
achievable approximation ratio) in the one-way variant
of our model is strictly different both from the
streaming complexity and the one-way communication
complexity thereof.",
acknowledgement = ack-nhfb,
articleno = "19",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Ganardi:2019:UTB,
author = "Moses Ganardi and Markus Lohrey",
title = "A Universal Tree Balancing Theorem",
journal = j-TOCT,
volume = "11",
number = "1",
pages = "1:1--1:??",
month = jan,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3278158",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:09 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3278158",
abstract = "We present a general framework for balancing
expressions (terms) in the form of so-called tree
straight-line programs. The latter can be seen as
circuits over the free term algebra extended by
contexts (terms with a hole) and the operations, which
insert terms/contexts into contexts. In Ref. [16], it
was shown that one can compute for a given term of size
n in logspace a tree straight-line program of depth O
(log n ) and size O ( n / log n ). In the present
article, it is shown that the conversion can be done in
DLOGTIME-uniform TC$^0$. This allows reducing the term
evaluation problem over an arbitrary algebra A to the
term evaluation problem over a derived two-sorted
algebra F ( A ). Three applications are presented: (i)
an alternative proof for a recent result by Krebs et
al. [25] on the expression evaluation problem is given;
(ii) it is shown that expressions for an arbitrary
(possibly non-commutative) semiring can be transformed
in DLOGTIME-uniform TC$^0$ into equivalent circuits of
logarithmic depth and size O ( n / log n ); and, (iii)
a corresponding result for regular expressions is
shown.",
acknowledgement = ack-nhfb,
articleno = "1",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Kayal:2019:RFR,
author = "Neeraj Kayal and Vineet Nair and Chandan Saha and
S{\'e}bastien Tavenas",
title = "Reconstruction of Full Rank Algebraic Branching
Programs",
journal = j-TOCT,
volume = "11",
number = "1",
pages = "2:1--2:??",
month = jan,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3282427",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:09 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3282427",
abstract = "An algebraic branching program (ABP) A can be modelled
as a product expression $ X_1 \middot X_2 \ldots {} X_d
$, where $ X_1 $ and $ X_d $ are 1 $ \times $ w and w $
\times $ 1 matrices, respectively, and every other $
X_k $ is a w $ \times $ w matrix; the entries of these
matrices are linear forms in m variables over a field F
(which we assume to be either Q or a field of
characteristic poly( m )). The polynomial computed by A
is the entry of the 1 $ \times $ 1 matrix obtained from
the product $ \Pi_{k = 1}^d X_k $. We say A is a full
rank ABP if the $ w^2 (d - 2) + 2 w $ linear forms
occurring in the matrices $ X_1, X_2, \ldots {}, X_d $
are F-linearly independent. Our main result is a
randomized reconstruction algorithm for full rank ABPs:
Given blackbox access to an m -variate polynomial f of
degree at most m, the algorithm outputs a full rank ABP
computing f if such an ABP exists, or outputs ``no full
rank ABP exists'' (with high probability). The running
time of the algorithm is polynomial in $m$ and $ \beta
$, where $ \beta $ is the bit length of the
coefficients of $f$. The algorithm works even if $ X_k$
is a $ w_{k - 1} \times w_k$ matrix (with $ w_0 = w_d =
1$), and $ w = (w_1, \ldots {}, w_{d - 1})$ is unknown.
The result is obtained by designing a randomized
polynomial time equivalence test for the family of
iterated matrix multiplication polynomial IMM$_{w, d}$,
the (1, 1)-th entry of a product of d rectangular
symbolic matrices whose dimensions are according to $ w
\in N^{d - 1}$. At its core, the algorithm exploits a
connection between the irreducible invariant subspaces
of the Lie algebra of the group of symmetries of a
polynomial $f$ that is equivalent to IMM$_{w, d}$ and
the ``layer spaces'' of a full rank ABP computing f.
This connection also helps determine the group of
symmetries of IMM$_{w, d}$ and show that IMM$_{w, d}$
is characterized by its group of symmetries.",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Larose:2019:SHC,
author = "Beno{\^\i}t Larose and Barnaby Martin and Dani{\"e}l
Paulusma",
title = "Surjective H-Colouring over Reflexive Digraphs",
journal = j-TOCT,
volume = "11",
number = "1",
pages = "3:1--3:??",
month = jan,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3282431",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:09 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3282431",
abstract = "The Surjective H-Colouring problem is to test if a
given graph allows a vertex-surjective homomorphism to
a fixed graph H. The complexity of this problem has
been well studied for undirected (partially) reflexive
graphs. We introduce endo-triviality, the property of a
structure that all of its endomorphisms that do not
have range of size 1 are automorphisms, as a means to
obtain complexity-theoretic classifications of
Surjective H-Colouring in the case of reflexive
digraphs. Chen (2014) proved, in the setting of
constraint satisfaction problems, that Surjective
H-Colouring is NP-complete if H has the property that
all of its polymorphisms are essentially unary. We give
the first concrete application of his result by showing
that every endo-trivial reflexive digraph H has this
property. We then use the concept of endo-triviality to
prove, as our main result, a dichotomy for Surjective
H-Colouring when H is a reflexive tournament: if H is
transitive, then Surjective H-Colouring is in NL;
otherwise, it is NP-complete. By combining this result
with some known and new results, we obtain a complexity
classification for Surjective H-Colouring when H is a
partially reflexive digraph of size at most 3.",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Fulla:2019:CBS,
author = "Peter Fulla and Hannes Uppman and Stanislav
Zivn{\'y}",
title = "The Complexity of {Boolean} Surjective General-Valued
{CSPs}",
journal = j-TOCT,
volume = "11",
number = "1",
pages = "4:1--4:??",
month = jan,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3282429",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:09 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3282429",
abstract = "Valued constraint satisfaction problems (VCSPs) are
discrete optimisation problems with a $ (Q \cup
\infty)$-valued objective function given as a sum of
fixed-arity functions. In Boolean surjective VCSPs,
variables take on labels from $ D = \{ 0, 1 \} $, and
an optimal assignment is required to use both labels
from $D$. Examples include the classical global Min-Cut
problem in graphs and the Minimum Distance problem
studied in coding theory. We establish a dichotomy
theorem and thus give a complete complexity
classification of Boolean surjective VCSPs with respect
to exact solvability. Our work generalises the
dichotomy for $ \{ 0, \infty \} $-valued constraint
languages (corresponding to surjective decision CSPs)
obtained by Creignou and H{\'e}brard. For the
maximisation problem of $ Q_{\geq 0}$-valued surjective
VCSPs, we also establish a dichotomy theorem with
respect to approximability. Unlike in the case of
Boolean surjective (decision) CSPs, there appears a
novel tractable class of languages that is trivial in
the non-surjective setting. This newly discovered
tractable class has an interesting mathematical
structure related to downsets and upsets. Our main
contribution is identifying this class and proving that
it lies on the borderline of tractability. A crucial
part of our proof is a polynomial-time algorithm for
enumerating all near-optimal solutions to a generalised
Min-Cut problem, which might be of independent
interest.",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Iwama:2019:ROB,
author = "Kazuo Iwama and Atsuki Nagao",
title = "Read-Once Branching Programs for Tree Evaluation
Problems",
journal = j-TOCT,
volume = "11",
number = "1",
pages = "5:1--5:??",
month = jan,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3282433",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:09 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3282433",
abstract = "Toward the ultimate goal of separating L and P, Cook,
McKenzie, Wehr, Braverman, and Santhanam introduced the
Tree Evaluation Problem ( TEP ). For fixed integers h
and k > 0, FT$_h$ ( k ) is given as a complete, rooted
binary tree of height h, in which each root node is
associated with a function from [ k ]$^2$ to [ k ], and
each leaf node with a number in [ k ]. The value of an
internal node v is defined naturally; that is, if it
has a function f and the values of its two child nodes
are a and b, then the value of v is f ( a, b ). Our
task is to compute the value of the root node by
sequentially executing this function evaluation in a
bottom-up fashion. The problem is obviously in P, and,
if we could prove that any branching program solving
FT$^h$ ( k ) needs at least k$^{r (h)}$ states for any
unbounded function r, then this problem is not in L,
thus achieving our goal. The mentioned authors
introduced a restriction called thrifty against the
structure of BP's (i,e., against the algorithm for
solving the problem) and proved that any thrifty BP
needs \Omega ( k$^h$ ) states. This article proves a
similar lower bound for read-once branching programs,
which allows us to get rid of the restriction on the
order of nodes read by the BP that is the nature of the
thrifty restriction.",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Blais:2019:DTL,
author = "Eric Blais and Cl{\'e}ment L. Canonne and Tom Gur",
title = "Distribution Testing Lower Bounds via Reductions from
Communication Complexity",
journal = j-TOCT,
volume = "11",
number = "2",
pages = "6:1--6:??",
month = apr,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3305270",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:10 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3305270",
abstract = "We present a new methodology for proving distribution
testing lower bounds, establishing a connection between
distribution testing and the simultaneous message
passing (SMP) communication model. Extending the
framework of Blais, Brody, and Matulef [15], we show a
simple way to reduce (private-coin) SMP problems to
distribution testing problems. This method allows us to
prove new distribution testing lower bounds, as well as
to provide simple proofs of known lower bounds. Our
main result is concerned with testing identity to a
specific distribution, p, given as a parameter. In a
recent and influential work, Valiant and Valiant [55]
showed that the sample complexity of the aforementioned
problem is closely related to the l$_{2 / 3}$
-quasinorm of p. We obtain alternative bounds on the
complexity of this problem in terms of an arguably more
intuitive measure and using simpler proofs. More
specifically, we prove that the sample complexity is
essentially determined by a fundamental operator in the
theory of interpolation of Banach spaces, known as
Peetre's K-functional. We show that this quantity is
closely related to the size of the effective support of
p (loosely speaking, the number of supported elements
that constitute the vast majority of the mass of p ).
This result, in turn, stems from an unexpected
connection to functional analysis and refined
concentration of measure inequalities, which arise
naturally in our reduction.",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Cai:2019:GAG,
author = "Jin-Yi Cai and Michael Kowalczyk and Tyson Williams",
title = "Gadgets and Anti-Gadgets Leading to a Complexity
Dichotomy",
journal = j-TOCT,
volume = "11",
number = "2",
pages = "7:1--7:??",
month = apr,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3305272",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:10 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3305272",
abstract = "We introduce an idea called anti-gadgets for
reductions in complexity theory. These anti-gadgets are
presented as graph fragments, but their effect is
equivalent to erasing the presence of other graph
fragments, as if we had managed to include a negative
copy of a certain graph gadget. We use this idea to
prove a complexity dichotomy theorem for the partition
function Z(G) of spin systems over 3-regular directed
graphs G, $$ Z (G) = \Sigma_{ \sigma : V (G) \to \{ 0,
1 \} } \Pi_{(u, v) \in E (G)} f(\sigma (u), \sigma (v))
$$, where each edge is given a (not necessarily
symmetric) complex-valued binary function $ f : { 0,
1}^2 \to C $. We show that $ Z(G) $ is either
computable in polynomial time or \#P-hard, depending
explicitly on $f$. When the input graph $G$ is planar,
there is an additional class of polynomial time
computable partition functions $ Z(G)$, while
everything else remains \#P-hard. Furthermore, this
additional class is precisely those that can be
transformed by a holographic reduction to matchgates,
followed by the Fisher--Kasteleyn--Temperley algorithm
via Pfaffians.",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Dinesh:2019:CLB,
author = "Krishnamoorthy Dinesh and Sajin Koroth and Jayalal
Sarma",
title = "Characterization and Lower Bounds for Branching
Program Size using Projective Dimension",
journal = j-TOCT,
volume = "11",
number = "2",
pages = "8:1--8:??",
month = apr,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3305274",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:10 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3305274",
abstract = "We study projective dimension, a graph parameter,
denoted by pd( G ) for a bipartite graph G, introduced
by Pudl{\'a}k and R{\"o}dl (1992). For a Boolean
function f (on n bits), Pudl{\'a}k and R{\"o}dl
associated a bipartite graph G$_f$ and showed that size
of the optimal branching program computing f, denoted
by bpsize( f ), is at least pd( G$_f$ ) (also denoted
by pd( f )). Hence, proving lower bounds for pd( f )
implies lower bounds for bpsize( f ). Despite several
attempts (Pudl{\'a}k and R{\"o}dl (1992), R{\'o}nyai et
al. (2000)), proving super-linear lower bounds for
projective dimension of explicit families of graphs has
remained elusive. We observe that there exist a Boolean
function f for which the gap between the pd( f ) and
bpsize( f ) is 2$^{ \Omega (n)}$. Motivated by the
argument in Pudl{\'a}k and R{\"o}dl (1992), we define
two variants of projective dimension: projective
dimension with intersection dimension 1, denoted by
upd( f ), and bitwise decomposable projective
dimension, denoted by bitpdim( f ). We show the
following results: (a) We observe that there exist a
Boolean function f for which the gap between upd( f )
and bpsize( f ) is 2$^{ \Omega (n)}$. In contrast, we
also show that the bitwise decomposable projective
dimension characterizes size of the branching program
up to a polynomial factor. That is, there exists a
constant c > 0 and for any function f, bitpdim( f )/6
\leq bpsize( f ) \leq (bitpdim( f )) $^c$. (b) We
introduce a new candidate family of functions f for
showing super-polynomial lower bounds for bitpdim( f ).
As our main result, for this family of functions, we
demonstrate gaps between pd( f ) and the above two new
measures for f: pd( f ) = O ( \sqrt n ) upd( f ) =
\Omega ( n ) bitpdim( f ) = \Omega ( n$^{1.5}$ / log n
). We adapt Nechiporuk's techniques for our linear
algebraic setting to prove the best-known bpsize lower
bounds for bitpdim. Motivated by this linear algebraic
setting of our main result, we derive exponential lower
bounds for two restricted variants of pd( f ) and upd(
f ) by observing that they are exactly equal to
well-studied graph parameters-bipartite clique cover
number and bipartite partition number, respectively.",
acknowledgement = ack-nhfb,
articleno = "8",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Kerenidis:2019:MPP,
author = "Iordanis Kerenidis and Adi Ros{\'e}n and Florent
Urrutia",
title = "Multi-Party Protocols, Information Complexity and
Privacy",
journal = j-TOCT,
volume = "11",
number = "2",
pages = "9:1--9:??",
month = apr,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3313230",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:10 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3313230",
abstract = "We introduce a new information-theoretic measure,
which we call Public Information Complexity (PIC), as a
tool for the study of multi-party computation
protocols, and of quantities such as their
communication complexity, or the amount of randomness
they require in the context of information-theoretic
private computations. We are able to use this measure
directly in the natural asynchronous message-passing
peer-to-peer model and show a number of interesting
properties and applications of our new notion: The
Public Information Complexity is a lower bound on the
Communication Complexity and an upper bound on the
Information Complexity; the difference between the
Public Information Complexity and the Information
Complexity provides a lower bound on the amount of
randomness used in a protocol; any communication
protocol can be compressed to its Public Information
Cost; and an explicit calculation of the zero-error
Public Information Complexity of the k -party, n -bit
Parity function, where a player outputs the bitwise
parity of the inputs. The latter result also
establishes that the amount of randomness needed by a
private protocol that computes this function is \Omega
( n ).",
acknowledgement = ack-nhfb,
articleno = "9",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Ramya:2019:LBS,
author = "C. Ramya and B. V. Raghavendra Rao",
title = "Lower bounds for Sum and Sum of Products of Read-once
Formulas",
journal = j-TOCT,
volume = "11",
number = "2",
pages = "10:1--10:??",
month = apr,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3313232",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:10 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3313232",
abstract = "We study limitations of polynomials computed by
depth-2 circuits built over read-once formulas (ROFs).
In particular: (*) We prove a $ 2^{ \Omega (n)} $ lower
bound for the sum of ROFs computing the $ 2 n$-variate
polynomial in VP defined by Raz and Yehudayoff. (*) We
obtain a $ 2^{ \Omega (\sqrt {n})}$ lower bound on the
size of $ \Sigma \Pi^{[n^{1 / 15}]}$ arithmetic
circuits built over restricted ROFs of unbounded depth
computing the permanent of an $ n \times n$ matrix
(superscripts on gates denote bound on the fan-in). The
restriction is that the number of variables with +
gates as a parent in a proper sub formula of the ROF
has to be bounded by $ \sqrt {n}$. This proves an
exponential lower bound for a subclass of possibly
non-multilinear formulas of unbounded depth computing
the permanent polynomial. (*) We also show an
exponential lower bound for the above model against a
polynomial in VP. (*) Finally, we observe that the
techniques developed yield an exponential lower bound
on the size of $ \Sigma \Pi^{[N^{1 / 30}]}$ arithmetic
circuits built over syntactically multi-linear $ \Sigma
\Pi \Sigma^{[N^{1 / 4}]}$ arithmetic circuits computing
a product of variable disjoint linear forms on $N$
variables, where the superscripts on gates denote bound
on the fan-in. Our proof techniques are built on the
measure developed by Kumar et al. [14] and are based on
a non-trivial analysis of ROFs under random partitions.
Further, our results exhibit strengths and provide more
insight into the lower bound techniques introduced by
Raz [19].",
acknowledgement = ack-nhfb,
articleno = "10",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Kolay:2019:CCG,
author = "Sudeshna Kolay and Fahad Panolan and Saket Saurabh",
title = "Communication Complexity and Graph Families",
journal = j-TOCT,
volume = "11",
number = "2",
pages = "11:1--11:??",
month = apr,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3313234",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:10 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3313234",
abstract = "Given a graph G and a pair ( F$_1$, F$_2$ ) of graph
families, the function GDISJ$_{G, F 1}$, F$_2$ takes as
input, two induced subgraphs G$_1$ and G$_2$ of G, such
that G$_1$ \in F$_1$ and G$_2$ \in F$_2$ and returns 1
if V ( G$_1$ ) \cap V ( G$_2$ )= \oslash and 0
otherwise. We study the communication complexity of
this problem in the two-party model. In particular, we
look at pairs of hereditary graph families. We show
that the communication complexity of this function,
when the two graph families are hereditary, is
sublinear if and only if there are finitely many graphs
in the intersection of these two families. Then, using
concepts from parameterized complexity, we obtain
nuanced upper bounds on the communication complexity of
GDISJ$_{G, F 1}$, F$_2$ . A concept related to
communication protocols is that of a ( F$_1$, F$_2$
)-separating family of a graph G. A collection F of
subsets of V ( G ) is called a ( F$_1$, F$_2$ )-
separating family for G, if for any two vertex disjoint
induced subgraphs G$_1$ \in F$_1$, G$_2$ \in F$_2$,
there is a set F \in F with V ( G$_1$ ) \subseteq F and
V ( G$_2$ ) \cap F = \oslash . Given a graph G on n
vertices, for any pair ( F$_1$, F$_2$ ) of hereditary
graph families with sublinear communication complexity
for GDISJ$_{G, F 1}$, F$_2$, we give an enumeration
algorithm that finds a subexponential sized ( F$_1$,
F$_2$ )-separating family. In fact, we give an
enumeration algorithm that finds a 2$^{o (k)}$ n$^{O
(1)}$ sized ( F$_1$, F$_2$ )-separating family, where k
denotes the size of a minimum sized set S of vertices
such that V ( G )\ S has a bipartition ( V$_1$, V$_2$ )
with G [ V$_1$ ] \in F$_1$ and G [ V$_2$ ] \in F$_2$.
We exhibit a wide range of applications for these
separating families, to obtain combinatorial bounds,
enumeration algorithms, as well as exact and FPT
algorithms for several problems.",
acknowledgement = ack-nhfb,
articleno = "11",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Schoenebeck:2019:BWC,
author = "Grant Schoenebeck and Biaoshuai Tao",
title = "Beyond Worst-case (In)approximability of Nonsubmodular
Influence Maximization",
journal = j-TOCT,
volume = "11",
number = "3",
pages = "12:1--12:??",
month = jun,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3313904",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:10 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3313904",
abstract = "We consider the problem of maximizing the spread of
influence in a social network by choosing a fixed
number of initial seeds, formally referred to as the
influence maximization problem. It admits a
(1-1/e)-factor approximation algorithm if the influence
function is submodular. Otherwise, in the worst case,
the problem is NP-hard to approximate to within a
factor of N$^{1 - \epsilon }$. This article studies
whether this worst-case hardness result can be
circumvented by making assumptions about either the
underlying network topology or the cascade model. All
our assumptions are motivated by many real-life social
network cascades. First, we present strong
inapproximability results for a very restricted class
of networks called the (stochastic) hierarchical
blockmodel, a special case of the well-studied
(stochastic) blockmodel in which relationships between
blocks admit a tree structure. We also provide a
dynamic-programming-based polynomial time algorithm,
which optimally computes a directed variant of the
influence maximization problem on hierarchical
blockmodel networks. Our algorithm indicates that the
inapproximability result is due to the bidirectionality
of influence between agent-blocks. Second, we present
strong inapproximability results for a class of
influence functions that are ``almost'' submodular,
called 2-quasi-submodular. Our inapproximability
results hold even for any 2-quasi-submodular f fixed in
advance. This result also indicates that the
``threshold'' between submodularity and
nonsubmodularity is sharp, regarding the
approximability of influence maximization.",
acknowledgement = ack-nhfb,
articleno = "12",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Bonamy:2019:TLB,
author = "Marthe Bonamy and {\l}Ukasz Kowalik and Micha{\l}
Pilipczuk and Arkadiusz Soca{\l}a and Marcin Wrochna",
title = "Tight Lower Bounds for the Complexity of
Multicoloring",
journal = j-TOCT,
volume = "11",
number = "3",
pages = "13:1--13:??",
month = jun,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3313906",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:10 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3313906",
abstract = "In the multicoloring problem, also known as ( a: b )-
coloring or b-fold coloring, we are given a graph G and
a set of a colors, and the task is to assign a subset
of b colors to each vertex of G so that adjacent
vertices receive disjoint color subsets. This natural
generalization of the classic coloring problem (the b
=1 case) is equivalent to finding a homomorphism to the
Kneser graph KG$_{a, b}$ and gives relaxations
approaching the fractional chromatic number. We study
the complexity of determining whether a graph has an (
a: b )-coloring. Our main result is that this problem
does not admit an algorithm with runtime f ( b )c 2$^{o
(log b)c n}$ for any computable f(b) unless the
Exponential Time Hypothesis (ETH) fails. A ( b +1)$^n$
c poly( n )-time algorithm due to Nederlof [33] shows
that this is tight. A direct corollary of our result is
that the graph homomorphism problem does not admit a
2$^{O (n + h)}$ algorithm unless the ETH fails even if
the target graph is required to be a Kneser graph. This
refines the understanding given by the recent lower
bound of Cygan et al. [9]. The crucial ingredient in
our hardness reduction is the usage of detecting
matrices of Lindstr{\"o}m [28], which is a
combinatorial tool that, to the best of our knowledge,
has not yet been used for proving complexity lower
bounds. As a side result, we prove that the runtime of
the algorithms of Abasi et al. [1] and of Gabizon et
al. [14] for the r -monomial detection problem are
optimal under the ETH.",
acknowledgement = ack-nhfb,
articleno = "13",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Black:2019:MPU,
author = "Timothy Black",
title = "Monotone Properties of $k$-Uniform Hypergraphs Are
Weakly Evasive",
journal = j-TOCT,
volume = "11",
number = "3",
pages = "14:1--14:??",
month = jun,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3313908",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:10 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3313908",
abstract = "A Boolean function in n variables is weakly evasive if
its decision-tree complexity is \Omega ( n ). By k
-graphs, we mean k -uniform hypergraphs. A k-graph
property on v vertices is a Boolean function on n
=$^v_k$ variables corresponding to the k -subsets of a
v -set that is invariant under the v! permutations of
the v -set (isomorphisms of k -graphs). In 1976, Rivest
and Vuillemin proved that all nonconstant monotone
graph properties ( k = 2) are weakly evasive,
confirming a conjecture of Aanderaa and Rosenberg in
1973. Then, in 2013, Kulkarni, Qiao, and Sun (KQS)
proved the analogous result for 3-graphs. We extend
these results to k -graphs for every fixed k. From
this, we show that monotone Boolean functions invariant
under the action of a large primitive group are weakly
evasive. Although KQS employ the powerful topological
approach of Kahn et al. in 1984 combined with heavy
number theory, our argument is elementary and
self-contained (modulo some basic group theory).
Inspired by the outline of the KQS approach, we
formalize the general framework of ``orbit augmentation
sequences'' of sets with group actions. We show that a
parameter of such sequences, called the spacing, is a
lower bound on the decision-tree complexity for any
nontrivial monotone property that is \Gamma -invariant
for all groups \Gamma involved in the orbit
augmentation sequence, assuming all those groups are p
-groups. We develop operations on such sequences such
as composition and direct product that will provide
helpful machinery for our applications. We apply this
general technique to k -graphs via certain liftings of
k -graphs with wreath product action of p -groups.",
acknowledgement = ack-nhfb,
articleno = "14",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Aviv:2019:ELG,
author = "Nir Aviv and Amnon Ta-Shma",
title = "On the Entropy Loss and Gap of Condensers",
journal = j-TOCT,
volume = "11",
number = "3",
pages = "15:1--15:??",
month = jun,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3317691",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:10 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/hash.bib;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3317691",
abstract = "Many algorithms are proven to work under the
assumption that they have access to a source of random,
uniformly distributed bits. However, in practice,
sources of randomness are often imperfect, giving n
random bits that have only k < n min-entropy. The value
n --- k is called the entropy gap of the source.
Randomness condensers are hash functions that hash any
such source to a shorter source with reduced entropy
gap g. The goal is to lose as little entropy as
possible in this process. Condensers also have an error
parameter \epsilon and use a small seed of uniformly
distributed bits whose length we desire to minimize as
well. In this work, we study the exact dependencies
between the different parameters of seeded randomness
condensers. We obtain a non-explicit upper bound,
showing the existence of condensers with entropy loss
log (1+log 1/ \epsilon / g ) + O (1) and seed length
log ( n --- k / \epsilon g ) + O (1). In particular,
this implies the existence of condensers with O (log 1
/ \epsilon ) entropy gap and constant entropy loss.
This extends (with slightly improved parameters) the
non-explicit upper bound for condensers presented in
the work of Dodis et al. (2014), which gives condensers
with entropy loss at least log log 1 / \epsilon . We
also give a non-explicit upper bound for lossless
condensers, which have entropy gap g \geq log 1 /
\epsilon / \epsilon + O (1) and seed length log ( n ---
k / \epsilon $^2$ g ) + O (1). Furthermore, we address
an open question raised in (Dodis et al. 2014), where
Dodis et al. showed an explicit construction of
condensers with constant gap and O (log log 1/ \epsilon
) loss, using seed length O ( n log 1 / \epsilon ). In
the same article they improve the seed length to O ( k
log k ) and ask whether it can be further improved. In
this work, we reduce the seed length of their
construction to O (log ( n / \epsilon )log ( k /
\&epsiv)) by a simple concatenation. In the
analysis, we use and prove a tight equivalence between
condensers and extractors with multiplicative error. We
note that a similar, but non-tight, equivalence was
already proven by Dodis et al. (Dodis et al. 2014)
using a weaker variant of extractors called
unpredictability extractors. We also remark that this
equivalence underlies the work of Ben-Aroya et al.
(Ben-Aroya et al. 2016) and later work on explicit
two-source extractors, and we believe it is interesting
in its own right.",
acknowledgement = ack-nhfb,
articleno = "15",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Aydinlioglu:2019:CAR,
author = "Baris Aydinlioglu and Eric Bach",
title = "Corrigendum to Affine Relativization: Unifying the
Algebrization and Relativization Barriers",
journal = j-TOCT,
volume = "11",
number = "3",
pages = "16:1--16:??",
month = jun,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3317693",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:10 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3317693",
acknowledgement = ack-nhfb,
articleno = "16",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Goldreich:2019:SLT,
author = "Oded Goldreich and Tom Gur and Ilan Komargodski",
title = "Strong Locally Testable Codes with Relaxed Local
Decoders",
journal = j-TOCT,
volume = "11",
number = "3",
pages = "17:1--17:??",
month = jun,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3319907",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:10 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3319907",
abstract = "Locally testable codes (LTCs) are error-correcting
codes that admit very efficient codeword tests. An LTC
is said to be strong if it has a proximity-oblivious
tester, that is, a tester that makes only a constant
number of queries and rejects non-codewords with a
probability that depends solely on their distance from
the code. Locally decodable codes (LDCs) are
complementary to LTCs. While the latter allow for
highly efficient rejection of strings that are far from
being codewords, LDCs allow for highly efficient
recovery of individual bits of the information that is
encoded in strings that are close to being codewords.
Constructions of strong-LTCs with nearly-linear length
are known, but the existence of a constant-query LDC
with polynomial length is a major open problem. In an
attempt to bypass this barrier, Ben-Sasson et al.
(SICOMP 2006) introduced a natural relaxation of local
decodability, called relaxed-LDCs. This notion requires
local recovery of nearly all individual
information-bits, yet allows for recovery-failure (but
not error) on the rest. Ben-Sasson et al. constructed a
constant-query relaxed-LDC with nearly-linear length
(i.e., length k$^{1 + \alpha }$ for an arbitrarily
small constant \alpha > 0, where k is the dimension of
the code). This work focuses on obtaining strong
testability and relaxed decodability simultaneously. We
construct a family of binary linear codes of
nearly-linear length that are both strong-LTCs (with
one-sided error) and constant-query relaxed-LDCs. This
improves upon the previously known constructions, which
either obtain only weak LTCs or require polynomial
length. Our construction heavily relies on tensor codes
and PCPs. In particular, we provide strong canonical
PCPs of proximity for membership in any linear code
with constant rate and relative distance. Loosely
speaking, these are PCPs of proximity wherein the
verifier is proximity oblivious (similarly to
strong-LTCs) and every valid statement has a unique
canonical proof. Furthermore, the verifier is required
to reject non-canonical proofs (even for valid
statements). As an application, we improve the best
known separation result between the complexity of
decision and verification in the setting of property
testing.",
acknowledgement = ack-nhfb,
articleno = "17",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Agrawal:2019:SCU,
author = "Akanksha Agrawal and Daniel Lokshtanov and Saket
Saurabh and Meirav Zehavi",
title = "Split Contraction: The Untold Story",
journal = j-TOCT,
volume = "11",
number = "3",
pages = "18:1--18:??",
month = jun,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3319909",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:10 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3319909",
abstract = "The edit operation that contracts edges, which is a
fundamental operation in the theory of graph minors,
has recently gained substantial scientific attention
from the viewpoint of Parameterized Complexity. In this
article, we examine an important family of graphs,
namely, the family of split graphs, which in the
context of edge contractions is proven to be
significantly less obedient than one might expect.
Formally, given a graph G and an integer k, S PLIT
CONTRACTION asks whether there exists X \subseteq E ( G
) such that G / X is a split graph and | X | \leq k.
Here, G / X is the graph obtained from G by contracting
edges in X. Guo and Cai [Theoretical Computer Science,
2015] claimed that SPLIT CONTRACTION is fixed-parameter
tractable. However, our findings are different. We show
that SPLIT CONTRACTION, despite its deceptive
simplicity, is W[1]-hard. Our main result establishes
the following conditional lower bound: Under the
Exponential Time Hypothesis, SPLIT CONTRACTION cannot
be solved in time 2$^o$ (l$^2$ )$ \cdot $ n$^O$ (1),
where l is the vertex cover number of the input graph.
We also verify that this lower bound is essentially
tight. To the best of our knowledge, this is the first
tight lower bound of the form 2$^o$ (l$^2$ )$ \cdot $
n$^{O (1)}$ for problems parameterized by the vertex
cover number of the input graph. In particular, our
approach to obtain this lower bound borrows the notion
of harmonious coloring from Graph Theory, and might be
of independent interest.",
acknowledgement = ack-nhfb,
articleno = "18",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Viola:2019:CEP,
author = "Emanuele Viola",
title = "Constant-Error Pseudorandomness Proofs from Hardness
Require Majority",
journal = j-TOCT,
volume = "11",
number = "4",
pages = "19:1--19:??",
month = sep,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3322815",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:11 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3322815",
abstract = "Research in the 1980s and 1990s showed how to
construct a pseudorandom generator from a function that
is hard to compute on more than 99\% of the inputs. A
more recent line of works showed, however, that if the
generator has small error, then the proof of
correctness cannot be implemented in subclasses of
TC$^0$, and hence the construction cannot be applied to
the known hardness results. This article considers a
typical class of pseudorandom generator constructions,
and proves an analogous result for the case of large
error.",
acknowledgement = ack-nhfb,
articleno = "19",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Haviv:2019:MFS,
author = "Ishay Haviv",
title = "On Minrank and Forbidden Subgraphs",
journal = j-TOCT,
volume = "11",
number = "4",
pages = "20:1--20:??",
month = sep,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3322817",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:11 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3322817",
abstract = "The minrank over a field $F$ of a graph $G$ on the
vertex set $ \{ 1, 2, \ldots, n \} $ is the minimum
possible rank of a matrix $ M \in F^{n \times n}$ such
that $ M_{i, i} \neq 0$ for every $i$, and $ M_{i, j} =
0$ for every distinct non-adjacent vertices $i$ and $j$
in $G$. For an integer $n$, a graph $H$, and a field
$F$, let $ g(n, H, F)$ denote the maximum possible
minrank over $F$ of an $n$-vertex graph whose
complement contains no copy of $H$. In this article, we
study this quantity for various graphs $H$ and fields
$F$. For finite fields, we prove by a probabilistic
argument a general lower bound on $ g(n, H, F)$, which
yields a nearly tight bound of $ \Omega (\sqrt n / l o
g n)$ for the triangle $ H = K_3$. For the real field,
we prove by an explicit construction that for every
non-bipartite graph $H$, $ g(n, H, R) \geq n^\delta $
for some $ \delta = \delta (H) > 0$. As a by-product of
this construction, we disprove a conjecture of
Codenotti et al. [11]. The results are motivated by
questions in information theory, circuit complexity,
and geometry.",
acknowledgement = ack-nhfb,
articleno = "20",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Boppana:2019:BIV,
author = "Ravi Boppana and Johan H{\aa}stad and Chin Ho Lee and
Emanuele Viola",
title = "Bounded Independence versus Symmetric Tests",
journal = j-TOCT,
volume = "11",
number = "4",
pages = "21:1--21:??",
month = sep,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3337783",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:11 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3337783",
abstract = "For a test T \subseteq {0, 1}$^n$, define k$^*$ ( T )
to be the maximum k such that there exists a k -wise
uniform distribution over {0, 1}$^n$ whose support is a
subset of T. For H$_t$ = { x \in 0, 1$^n$: | \Sigma
$_i$ x$_i$ --- n /2| $<$ = t }, we prove k$^*$ ( H$_t$
) = \Theta ( t$^2$ / n + 1). For S$_{m, c}$ = { x \in
0, 1$^n$: \Sigma $_i$ x$_i$ \equiv c (mod m )}, we
prove that k$^*$ ( S$_{m, c}$ ) = \Theta ( n / m$^2$ ).
For some k = O ( n / m ) we also show that any k -wise
uniform distribution puts probability mass at most 1/ m
+ 1/100 over S$_{m, c}$. Finally, for any fixed odd m
we show that there is an integer k = (1 --- \Omega (1))
n such that any k -wise uniform distribution lands in T
with probability exponentially close to | S$_{m, c}$
|/2$^n$; and this result is false for any even m.",
acknowledgement = ack-nhfb,
articleno = "21",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Oliveira:2019:RMB,
author = "Mateus {De Oliveira Oliveira} and Pavel Pudl{\'a}k",
title = "Representations of Monotone {Boolean} Functions by
Linear Programs",
journal = j-TOCT,
volume = "11",
number = "4",
pages = "22:1--22:??",
month = sep,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3337787",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:11 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3337787",
abstract = "We introduce the notion of monotone linear programming
circuits (MLP circuits), a model of computation for
partial Boolean functions. Using this model, we prove
the following results.$^1$ (1) MLP circuits are
superpolynomially stronger than monotone Boolean
circuits. (2) MLP circuits are exponentially stronger
than monotone span programs over the reals. (3) MLP
circuits can be used to provide monotone feasibility
interpolation theorems for Lov{\'a}sz-Schrijver proof
systems and for mixed Lov{\'a}sz-Schrijver proof
systems. (4) The Lov{\'a}sz-Schrijver proof system
cannot be polynomially simulated by the cutting planes
proof system. Finally, we establish connections between
the problem of proving lower bounds for the size of MLP
circuits and the field of extension complexity of
polytopes.",
acknowledgement = ack-nhfb,
articleno = "22",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Goldberg:2019:APC,
author = "Leslie Ann Goldberg and Mark Jerrum",
title = "Approximating Pairwise Correlations in the {Ising}
Model",
journal = j-TOCT,
volume = "11",
number = "4",
pages = "23:1--23:??",
month = sep,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3337785",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:11 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3337785",
abstract = "In the Ising model, we consider the problem of
estimating the covariance of the spins at two specified
vertices. In the ferromagnetic case, it is easy to
obtain an additive approximation to this covariance by
repeatedly sampling from the relevant Gibbs
distribution. However, we desire a multiplicative
approximation, and it is not clear how to achieve this
by sampling, given that the covariance can be
exponentially small. Our main contribution is a fully
polynomial time randomised approximation scheme (FPRAS)
for the covariance in the ferromagnetic case. We also
show that the restriction to the ferromagnetic case is
essential-there is no FPRAS for multiplicatively
estimating the covariance of an antiferromagnetic Ising
model unless RP = \#P. In fact, we show that even
determining the sign of the covariance is \#P-hard in
the antiferromagnetic case.",
acknowledgement = ack-nhfb,
articleno = "23",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Blais:2019:TJT,
author = "Eric Blais and Cl{\'e}ment L. Canonne and Talya Eden
and Amit Levi and Dana Ron",
title = "Tolerant Junta Testing and the Connection to
Submodular Optimization and Function Isomorphism",
journal = j-TOCT,
volume = "11",
number = "4",
pages = "24:1--24:??",
month = sep,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3337789",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:11 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3337789",
abstract = "A function $ f : \{ - 1, 1 \}^n \to \{ - 1, 1 \} $ is
a $k$-junta if it depends on at most $k$ of its
variables. We consider the problem of tolerant testing
of $k$ juntas, where the testing algorithm must accept
any function that is $ \epsilon $-close to some
$k$-junta and reject any function that is $ \epsilon
'$-far from every $ k'$-junta for some $ \epsilon ' =
O(\epsilon)$ and $ k' = O(k)$. Our first result is an
algorithm that solves this problem with query
complexity polynomial in $k$ and $ 1 / \epsilon $. This
result is obtained via a new polynomial-time
approximation algorithm for submodular function
minimization (SFM) under large cardinality constraints,
which holds even when only given an approximate oracle
access to the function. Our second result considers the
case where $ k' = k$. We show how to obtain a smooth
tradeoff between the amount of tolerance and the query
complexity in this setting. Specifically, we design an
algorithm that, given $ \rho \in (0, 1)$, accepts any
function that is $ \epsilon \rho / 16$-close to some
$k$-junta and rejects any function that is $ \epsilon
$-far from every $k$-junta. The query complexity of the
algorithm is $ O(k \log k / \epsilon \rho (1 -
\rho)^k)$. Finally, we show how to apply the second
result to the problem of tolerant isomorphism testing
between two unknown Boolean functions $f$ and $g$. We
give an algorithm for this problem whose query
complexity only depends on the (unknown) smallest $k$
such that either $f$ or $g$ is close to being a
$k$-junta.",
acknowledgement = ack-nhfb,
articleno = "24",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Scheder:2019:PMB,
author = "Dominik Scheder",
title = "{PPSZ} for $ k \geq 5 $: More Is Better",
journal = j-TOCT,
volume = "11",
number = "4",
pages = "25:1--25:??",
month = sep,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3349613",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:11 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3349613",
abstract = "We show that for k \geq 5, the PPSZ algorithm for k
-SAT runs exponentially faster if there is an
exponential number of satisfying assignments. More
precisely, we show that for every k \geq 5, there is a
strictly increasing function f: [0,1] -{$>$} R with f
(0) = 0 that has the following property. If F is a k
-CNF formula over n variables and |sat(F)| = 2$^{
\delta n}$ solutions, then PPSZ finds a satisfying
assignment with probability at least 2$^{- c k n - - -
o (n) + f (\delta) n}$. Here, 2$^{- c k n - o (n)}$ is
the success probability proved by Paturi et al. [11]
for k -CNF formulas with a unique satisfying
assignment. Our proof rests on a combinatorial lemma:
given a set S \subseteq { 0,1}$^n$, we can partition {
0,1}$^n$ into subcubes such that each subcube B
contains exactly one element of S. Such a partition B
induces a distribution on itself, via Pr [ B ] = |B| /
2$^n$ for each B \in B. We are interested in partitions
that induce a distribution of high entropy. We show
that, in a certain sense, the worst case (min$_{S : |S|
= s}$ max$_B$ H ( B )) is achieved if S is a Hamming
ball. This lemma implies that every set S of
exponential size allows a partition of linear entropy.
This in turn leads to an exponential improvement of the
success probability of PPSZ.",
acknowledgement = ack-nhfb,
articleno = "25",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Beyersdorff:2019:NRB,
author = "Olaf Beyersdorff and Leroy Chew and Mikol{\'a}s
Janota",
title = "New Resolution-Based {QBF} Calculi and Their Proof
Complexity",
journal = j-TOCT,
volume = "11",
number = "4",
pages = "26:1--26:??",
month = sep,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3352155",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:11 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3352155",
abstract = "Modern QBF solvers typically use two different
paradigms, conflict-driven clause learning (CDCL)
solving or expansion solving. Proof systems for
quantified Boolean formulas (QBFs) provide a
theoretical underpinning for the performance of these
solvers, with Q-Resolution and its extensions relating
to CDCL solving and \forall Exp+Res relating to
expansion solving. This article defines two novel
calculi, which are resolution-based and enable
unification of some of the principal existing
resolution-based QBF calculi, namely Q-resolution,
long-distance Q-resolution and the expansion-based
calculus \forall Exp+Res. However, the proof complexity
of the QBF resolution proof systems is currently not
well understood. In this article, we completely
determine the relative power of the main QBF resolution
systems, settling in particular the relationship
between the two different types of resolution-based QBF
calculi: proof systems for CDCL-based solvers
(Q-resolution, universal, and long-distance
Q-resolution) and proof systems for expansion-based
solvers ( \forall Exp+Res and its generalizations
IR-calc and IRM-calc defined here). The most
challenging part of this comparison is to exhibit hard
formulas that underlie the exponential separations of
the aforementioned proof systems. To this end, we
exhibit a new and elegant proof technique for showing
lower bounds in QBF proof systems based on strategy
extraction. This technique provides a direct transfer
of circuit lower bounds to lengths-of-proofs lower
bounds. We use our method to show the hardness of a
natural class of parity formulas for Q-resolution and
universal Q-resolution. Variants of the formulas are
hard for even stronger systems such as long-distance
Q-resolution and extensions. With a completely
different and novel counting argument, we show the
hardness of the prominent formulas of Kleine B{\"u}ning
et al. [51] for the strong expansion-based calculus
IR-calc.",
acknowledgement = ack-nhfb,
articleno = "26",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Allender:2019:NIN,
author = "Eric Allender and Shuichi Hirahara",
title = "New Insights on the (Non-)Hardness of Circuit
Minimization and Related Problems",
journal = j-TOCT,
volume = "11",
number = "4",
pages = "27:1--27:??",
month = sep,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3349616",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:11 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3349616",
abstract = "The Minimum Circuit Size Problem (MCSP) and a related
problem (MKTP) that deal with time-bounded Kolmogorov
complexity are prominent candidates for NP-intermediate
status. We show that, under very modest cryptographic
assumptions (such as the existence of one-way
functions), the problem of approximating the minimum
circuit size (or time-bounded Kolmogorov complexity)
within a factor of n$^{1 - o (1)}$ is indeed
NP-intermediate. To the best of our knowledge, these
problems are the first natural NP-intermediate problems
under the existence of an arbitrary one-way function.
Our technique is quite general; we use it also to show
that approximating the size of the largest clique in a
graph within a factor of n$^{1 - o (1)}$ is also
NP-intermediate unless NP \subseteq P/poly. We also
prove that MKTP is hard for the complexity class DET
under non-uniform NC$^0$ reductions. This is
surprising, since prior work on MCSP and MKTP had
highlighted weaknesses of ``local'' reductions such as
\leq $^{NC 0}$ $_m$. We exploit this local reduction to
obtain several new consequences: --- MKTP is not in
AC$^0$ [ p ]. --- Circuit size lower bounds are
equivalent to hardness of a relativized version
MKTP$^A$ of MKTP under a class of uniform AC$^0$
reductions, for a significant class of sets A. ---
Hardness of MCSP$^A$ implies hardness of MCSP$^A$ for a
significant class of sets A. This is the first result
directly relating the complexity of MCSP$^A$ and
MCSP$^A$, for any A.",
acknowledgement = ack-nhfb,
articleno = "27",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{Jansen:2019:OSS,
author = "Bart M. P. Jansen and Astrid Pieterse",
title = "Optimal Sparsification for Some Binary {CSPs} Using
Low-Degree Polynomials",
journal = j-TOCT,
volume = "11",
number = "4",
pages = "28:1--28:??",
month = sep,
year = "2019",
CODEN = "????",
DOI = "https://doi.org/10.1145/3349618",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Tue Oct 22 10:25:11 MDT 2019",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/ft_gateway.cfm?id=3349618",
abstract = "This article analyzes to what extent it is possible to
efficiently reduce the number of clauses in NP-hard
satisfiability problems without changing the answer.
Upper and lower bounds are established using the
concept of kernelization. Existing results show that if
NP $ \not \subseteq $ coNP/poly, no efficient
preprocessing algorithm can reduce $n$-variable
instances of cnf-sat with d literals per clause to
equivalent instances with O ( n$^{d - \epsilon }$ )
bits for any \epsilon > 0. For the Not-All-Equal sat
problem, a compression to size {\~O} ( n$^{d - 1}$ )
exists. We put these results in a common framework by
analyzing the compressibility of CSPs with a binary
domain. We characterize constraint types based on the
minimum degree of multivariate polynomials whose roots
correspond to the satisfying assignments, obtaining
(nearly) matching upper and lower bounds in several
settings. Our lower bounds show that not just the
number of constraints, but also the encoding size of
individual constraints plays an important role. For
example, for Exact Satisfiability with unbounded clause
length it is possible to efficiently reduce the number
of constraints to n +1, yet no polynomial-time
algorithm can reduce to an equivalent instance with O (
n$^{2 - \epsilon }$ ) bits for any \epsilon > 0, unless
NP \subseteq coNP/poly.",
acknowledgement = ack-nhfb,
articleno = "28",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1190",
}
@Article{ODonnell:2020:ENE,
author = "Ryan O'Donnell",
title = "Editorial from the New {Editor-in-Chief}",
journal = j-TOCT,
volume = "12",
number = "1",
pages = "1e:1--1e:1",
month = feb,
year = "2020",
CODEN = "????",
DOI = "https://doi.org/10.1145/3381517",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Feb 26 07:25:37 MST 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3381517",
acknowledgement = ack-nhfb,
articleno = "1e",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "https://dl.acm.org/loi/toct",
}
@Article{Ghosh:2020:FAE,
author = "Arijit Ghosh and Sudeshna Kolay and Gopinath Mishra",
title = "{FPT} Algorithms for Embedding into Low-Complexity
Graphic Metrics",
journal = j-TOCT,
volume = "12",
number = "1",
pages = "1:1--1:41",
month = feb,
year = "2020",
CODEN = "????",
DOI = "https://doi.org/10.1145/3369933",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Feb 26 07:25:37 MST 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3369933",
abstract = "Given metric spaces $ (X, D_X) $ and $ (Y, D_Y) $, an
embedding $ F : X \to Y $ is an injective mapping from
X to Y. Expansion e_F and contraction c_F of an
embedding $ F : X \to Y $ are defined as $ e_F = m a
x_{x_{; 1}, x_2 (\neq x1) \in X} D_Y(F(x_1), F(x_2)) /
D_X(x_1, x_2) $ and $ c_F = m a x_{x_1, x_2 (\neq x_1)
\in X} D_X(x_1, x_2) / D_Y(F(x_1), F(x_2)) $,
respectively, and distortion $ d_F $ is defined as $
d_F = e_F \cdot c_F $. Observe that $ d_F \geq 1 $. An
embedding $ F : X \to Y $ is noncontracting if $ c_F
\leq 1 $. When $ d = 1 $, then $F$ is isometry.\par
The Metric Embedding problem takes as input two metric
spaces $ (X, D_X)$ and $ (Y, D_Y)$, and a positive
integer $d$. The objective is to determine whether
there is an embedding $ F : X \to Y$ such that $ d_F
\leq d$. Such an embedding is called a distortion $d$
embedding. The bijective Metric Embedding problem is a
special case of the Metric Embedding problem where $ X
= Y $. In parameterized complexity, the Metric
Embedding problem, in full generality, is known to be
$W$-hard and, therefore, not expected to have an FPT
algorithm. In this article, we consider the Gen-Graph
Metric Embedding problem, where the two metric spaces
are graph metrics. We explore the extent of
tractability of the problem in the parameterized
complexity setting. We determine whether an unweighted
graph metric $ (G, D_G)$ can be embedded, or
bijectively embedded, into another unweighted graph
metric $ (H, D_H)$, where the graph $H$ has low
structural complexity. For example, $H$ is a cycle, or
$H$ has bounded treewidth or bounded connected
treewidth. The parameters for the algorithms are chosen
from the upper bound $d$ on distortion, bound $ \Delta
$ on the maximum degree of $H$, treewidth $ \alpha $ of
$H$, and connected treewidth $ \alpha_c$ of
$H$.\par
Our general approach to these problems can be
summarized as trying to understand the behavior of the
shortest paths in $G$ under a low-distortion embedding
into $H$, and the structural relation the mapping of
these paths has to shortest paths in $H$.",
acknowledgement = ack-nhfb,
articleno = "1",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "https://dl.acm.org/loi/toct",
}
@Article{Kayal:2020:SBR,
author = "Neeraj Kayal and Vineet Nair and Chandan Saha",
title = "Separation Between Read-once Oblivious Algebraic
Branching Programs {(ROABPs)} and Multilinear
Depth-three Circuits",
journal = j-TOCT,
volume = "12",
number = "1",
pages = "2:1--2:27",
month = feb,
year = "2020",
CODEN = "????",
DOI = "https://doi.org/10.1145/3369928",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Feb 26 07:25:37 MST 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3369928",
abstract = "We show an exponential separation between two
well-studied models of algebraic computation, namely,
read-once oblivious algebraic branching programs
(ROABPs) and multilinear depth-three circuits. In
particular, we show the following: (1) There exists an
\ldots{}",
acknowledgement = ack-nhfb,
articleno = "2",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "https://dl.acm.org/loi/toct",
}
@Article{Hemaspaandra:2020:SVD,
author = "Edith Hemaspaandra and Lane A. Hemaspaandra and Curtis
Menton",
title = "Search versus Decision for Election Manipulation
Problems",
journal = j-TOCT,
volume = "12",
number = "1",
pages = "3:1--3:42",
month = feb,
year = "2020",
CODEN = "????",
DOI = "https://doi.org/10.1145/3369937",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Feb 26 07:25:37 MST 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3369937",
abstract = "Most theoretical definitions about the complexity of
manipulating elections focus on the decision problem of
recognizing which instances can be successfully
manipulated rather than the search problem of finding
the successful manipulative actions. Since \ldots{}",
acknowledgement = ack-nhfb,
articleno = "3",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "https://dl.acm.org/loi/toct",
}
@Article{Hermo:2020:ELB,
author = "Montserrat Hermo and Ana Ozaki",
title = "Exact Learning: On the Boundary between {Horn} and
{CNF}",
journal = j-TOCT,
volume = "12",
number = "1",
pages = "4:1--4:25",
month = feb,
year = "2020",
CODEN = "????",
DOI = "https://doi.org/10.1145/3369930",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Feb 26 07:25:37 MST 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3369930",
abstract = "A major problem in computational learning theory is
whether the class of formulas in conjunctive normal
form (CNF) is efficiently learnable. Although it is
known that this class cannot be polynomially learned
using either membership or equivalence \ldots{}",
acknowledgement = ack-nhfb,
articleno = "4",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "https://dl.acm.org/loi/toct",
}
@Article{Kumar:2020:PBD,
author = "Mrinal Kumar",
title = "On the Power of Border of Depth-3 Arithmetic
Circuits",
journal = j-TOCT,
volume = "12",
number = "1",
pages = "5:1--5:8",
month = feb,
year = "2020",
CODEN = "????",
DOI = "https://doi.org/10.1145/3371506",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Feb 26 07:25:37 MST 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3371506",
abstract = "We show that over the field of complex numbers, every
homogeneous polynomial of degree d can be approximated
(in the border complexity sense) by a depth-3
arithmetic circuit of top fan-in at most 2. This is
quite surprising, since there exist \ldots{}",
acknowledgement = ack-nhfb,
articleno = "5",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "https://dl.acm.org/loi/toct",
}
@Article{Fernau:2020:PMV,
author = "Henning Fernau and Florin Manea and Robert Mercas and
Markus L. Schmid",
title = "Pattern Matching with Variables: Efficient Algorithms
and Complexity Results",
journal = j-TOCT,
volume = "12",
number = "1",
pages = "6:1--6:37",
month = feb,
year = "2020",
CODEN = "????",
DOI = "https://doi.org/10.1145/3369935",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Feb 26 07:25:37 MST 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3369935",
abstract = "A pattern $ \alpha $ (i.e., a string of variables and
terminals) matches a word $w$, if $w$ can be obtained
by uniformly replacing the variables of $ \alpha $ by
terminal words. The respective matching problem, i.e.,
deciding whether or not a given pattern matches a given
\ldots{}",
acknowledgement = ack-nhfb,
articleno = "6",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "https://dl.acm.org/loi/toct",
}
@Article{Goldenberg:2020:TGD,
author = "Elazar Goldenberg and Karthik C. S.",
title = "Toward a General Direct Product Testing Theorem",
journal = j-TOCT,
volume = "12",
number = "1",
pages = "7:1--7:18",
month = feb,
year = "2020",
CODEN = "????",
DOI = "https://doi.org/10.1145/3369939",
ISSN = "1942-3454 (print), 1942-3462 (electronic)",
ISSN-L = "1942-3454",
bibdate = "Wed Feb 26 07:25:37 MST 2020",
bibsource = "http://www.math.utah.edu/pub/tex/bib/toct.bib",
URL = "https://dl.acm.org/doi/abs/10.1145/3369939",
abstract = "The direct product encoding of a string $ a \in \{ 0,
1 \}^n $ on an underlying domain $ V \subseteq
(k^{[n]}) $ is a function DP$_V(a)$ that gets as input
a set $ S \in V$ and outputs a restricted to $S$. In
the direct product testing problem, we are given a
function $ F : V \to \{ 0, 1 \}^k$, and our goal is to
test whether $F$ is close to a direct product encoding
that is, whether there exists some $ a \in \{ 0, 1
\}^n$ such that on most sets $S$, we have $ F(S) = D
P_V(a)(S)$. A natural test is as follows: select a pair
$ (S, S) \in V$ according to some underlying
distribution over $ V \times V$, query $F$ on this
pair, and check for consistency on their intersection.
Note that the preceding distribution may be viewed as a
weighted graph over the vertex set $V$ and is referred
to as a test graph.\par
The testability of direct products was studied over
various domains and test graphs: Dinur and Steurer (CCC
14) analyzed it when $V$ equals the $k$-th slice of the
Boolean hypercube and the test graph is a member of the
Johnson graph family. Dinur and Kaufman (FOCS 17)
analyzed it for the case where V is the set of faces of
a Ramanujan complex, where in this case $ V = O_k(n)$.
In this article, we study the testability of direct
products in a general setting, addressing the question:
what properties of the domain and the test graph allow
one to prove a direct product testing
theorem?\par
Towards this goal, we introduce the notion of
coordinate expansion of a test graph. Roughly speaking,
a test graph is a coordinate expander if it has global
and local expansion, and has certain nice intersection
properties on sampling. We show that whenever the test
graph has coordinate expansion, it admits a direct
product testing theorem. Additionally, for every $k$
and $n$, we provide a direct product domain $ V
\subseteq (k^n)$ of size $n$, called the sliding window
domain, for which we prove direct product
testability.",
acknowledgement = ack-nhfb,
articleno = "7",
fjournal = "ACM Transactions on Computation Theory",
journal-URL = "https://dl.acm.org/loi/toct",
}