Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
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)
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Hardness Results for Coloring 3 -Colorable 3 -Uniform Hypergraphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A New Multilayered PCP and the Hardness of Hypergraph Vertex Cover
SIAM Journal on Computing
Noise stability of functions with low in.uences invariance and optimality
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Gowers uniformity, influence of variables, and PCPs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
More efficient queries in PCPs for NP and improved approximation hardness of maximum CSP
Random Structures & Algorithms
Conditional hardness for satisfiable 3-CSPs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Gowers Uniformity, Influence of Variables, and PCPs
SIAM Journal on Computing
Conditional Hardness of Approximating Satisfiable Max 3CSP-q
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Agnostic Learning of Monomials by Halfspaces Is Hard
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
NP-hardness of approximately solving linear equations over reals
Proceedings of the forty-third annual ACM symposium on Theory of computing
Bypassing UGC from some optimal geometric inapproximability results
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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
A new point of NP-hardness for unique games
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
On the Usefulness of Predicates
CCC '12 Proceedings of the 2012 IEEE Conference on Computational Complexity (CCC)
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We prove that for all integer k ≥ 3, there is a predicate P on k Boolean variables with 2~O(k1/3) accepting assignments that is approximation resistant even on satisfiable instances. That is, given a satisfiable CSP instance with constraint P, we cannot achieve better approximation ratio than simply picking random assignments. This improves the best previously known result by Hastad and Khot where the predicate has 2O(k1/2) accepting assignments. Our construction is inspired by several recent developments. One is the idea of using direct sums to improve soundness of PCPs, developed by Chan [5]. We also use techniques from Wenner [32] to construct PCPs with perfect completeness without relying on the d-to-1 Conjecture.