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More Efficient Queries in PCPs for NP and Improved Approximation Hardness of Maximum CSP
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
2008 (English)In: Random structures & algorithms (Print), ISSN 1042-9832, E-ISSN 1098-2418, Vol. 33, no 4, 497-514 p.Article in journal (Refereed) Published
Abstract [en]

Samorodnitsky and Trevisan [STOC 2000, pp. 191-199] proved that there exists, for every positive integer k, a PCP for NP with O(log n) randomness, query complexity 2k + k(2), free bit complexity 2k, completeness 1 - epsilon, and soundness 2(-k2) + epsilon. In this article, we devise a new "outer verifier," based on the layered label cover problem recently introduced by Dinur et al. [STOC 2003, pp. 595-601], and combine it with a new "inner verifier" that uses the query bits more efficiently than earlier verifiers. Our resulting theorem is that there exists, for every integer f >= 2, every positive integer t <= f (f - 1)/2, and every constant epsilon > 0, a PCP for NP with O(log n) randomness, query complexity f + t, free bit complexity f, completeness 1 - epsilon, and soundness 2(-t) + epsilon. As a corollary, there exists, for every integer q >= 3 and every constant epsilon > 0, a q-query PCP for NP with amortized query complexity 1 + root 2/q + epsilon-we also show in this article that combining our outer verifier with any natural candidate for a corresponding inner verifier gives a PCP that is kess query efficient than the one we obtain.

Place, publisher, year, edition, pages
2008. Vol. 33, no 4, 497-514 p.
Keyword [en]
probabilistic proof systems, maximum CSP, approximation hardness
National Category
Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-33173DOI: 10.1002/rsa.20226ISI: 000260844400005Scopus ID: 2-s2.0-60349121066OAI: oai:DiVA.org:kth-33173DiVA: diva2:413776
Note
QC 20110429Available from: 2011-04-29 Created: 2011-04-29 Last updated: 2017-12-11Bibliographically approved

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