Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Improved non-approximability results
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Recycling queries in PCPs and in linearity tests (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Simple analysis of graph tests for linearity and PCP
Random Structures & Algorithms
A new multilayered PCP and the hardness of hypergraph vertex cover
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Probabilistically Checkable Proofs with Low Amortized Query Complexity
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Query Efficient PCPs with Perfect Completeness
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
The Nonapproximability of Non-Boolean Predicates
SIAM Journal on Discrete Mathematics
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
More efficient queries in PCPs for NP and improved approximation hardness of maximum CSP
Random Structures & Algorithms
CSP gaps and reductions in the lasserre hierarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
Optimal Sherali-Adams Gaps from Pairwise Independence
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
A Hypergraph Dictatorship Test with Perfect Completeness
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Query-efficient dictatorship testing with perfect completeness
Property testing
Query-efficient dictatorship testing with perfect completeness
Property testing
Approximating Max kCSP - outperforming a random assignment with almost a linear factor
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
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In the PCP model, a verifier is supposed to probabilistically decide if a given input belongs to some language by posing queries to a purported proof of this fact. The probability that the verifier accepts an input in the language given a correct proof is called the completeness c; the probability that the verifier rejects an input not in the language given any proof is called the soundness s. For a verifier posing q queries to the proof, the amortized query complexity is defined by q / log2(c/s) if the proof is coded in binary. It is a measure of the average “efficiency” of the queries in the following sense: An ideal query should preserve the completeness and halve the soundness. If this were the case for all queries, the amortized query complexity would be exactly one. Samorodnitsky and Trevisan [STOC 2000] gave a q-query PCP for NP with amortized query complexity 1+2/ $\sqrt{q}+\varepsilon$ for any constant ε 0. In this paper, we examine to what extent their result can be sharpened. Using the layered label cover problem recently introduced by Dinur et al. [STOC 2003], we devise a new “outer verifier” that allows us to construct an “inner verifier” that uses the query bits more efficiently than earlier verifiers. This enables us to construct a PCP for NP that queries q positions in the proof and has amortized query complexity $1+2/ \sqrt{q}+\varepsilon$. As an immediate corollary, we also obtain an improved hardness of approximation result for the Maximum q-CSP problem. Since the improvement compared to previous work is moderate, we then examine if there is an underlying reason for this. Our construction in this paper follows a paradigm for query efficient PCPs for NP outlined by many previous researchers and it combines a state-of-the-art “outer verifier” with a natural candidate for a query efficient “inner verifier”. We prove in the full version of this paper that all natural attempts to construct more query efficient versions of our verifier are doomed to fail. This implies that significantly new ideas regarding proof composition and encoding of PCP proofs are required to construct PCPs for NP that are more query efficient than the one we propose in his paper.