License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2013.19
URN: urn:nbn:de:0030-drops-44011
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/4401/
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Khot, Subhash

On Approximation Resistance of Predicates (Invited Talk)

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Abstract

Constraint satisfaction problems are some of the most well-studied NP-hard problems, 3SAT being a prominent example. It is known by Hastad's 1997 result that 3SAT is "approximation resistant" in the following sense: given a near-satisfiable instance, a trivial algorithm that assigns random boolean values to the variables satisfies 7/8 fraction of the constraints and no efficient algorithm can do strictly better unless P=NP!

3SAT is a CSP that corresponds to the ternary OR predicate. In general, a CSP has constraints given by some fixed predicate P:{0,1}^k -> {True, False} (on possibly negated variables) and the predicate is called approximation resistant if, on a near-satisfiable instance, it is computationally hard to perform strictly better than a random assignment.

The quest to understand approximation resistance has played a central role in the theory of probabilistically checkable proofs (PCPs) and hardness of approximation. This talk will give a survey of the topic, including recent work giving a complete characterization of approximation resistance (i.e. a necessary and sufficient condition on the predicate that makes the corresponding CSP approximation resistant).

BibTeX - Entry

@InProceedings{khot:LIPIcs:2013:4401,
  author =	{Subhash Khot},
  title =	{{On Approximation Resistance of Predicates (Invited Talk)}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{19--19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Anil Seth and Nisheeth K. Vishnoi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/4401},
  URN =		{urn:nbn:de:0030-drops-44011},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.19},
  annote =	{Keywords: Approximation resistance, Hardness of approximation, Probabilistically checkable proofs, Constraint satisfaction problem}
}

Keywords: Approximation resistance, Hardness of approximation, Probabilistically checkable proofs, Constraint satisfaction problem
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)
Issue Date: 2013
Date of publication: 10.12.2013

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