More Efficient Queries in PCPs for NP and Improved Approximation Hardness of Maximum CSP
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   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. (C) 2008 Wiley Periodicals, Inc. Random Struct. Alg., 33, 497-514, 2008
approximation hardness maximum csp probabilistic proof systems