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
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)
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation algorithms
Some optimal inapproximability results
Journal of the ACM (JACM)
Journal of Computer and System Sciences
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Simple analysis of graph tests for linearity and PCP
Random Structures & Algorithms
Optimal Inapproximability Results for Max-Cut and Other 2-Variable CSPs?
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Testing Polynomials over General Fields
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Testing Low-Degree Polynomials over Prime Fields
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
On the Hardness of Approximating Multicut and Sparsest-Cut
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Linearity testing in characteristic two
IEEE Transactions on Information Theory - Part 1
Balanced max 2-sat might not be the hardest
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Low-degree tests at large distances
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Near-optimal algorithms for maximum constraint satisfaction problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Unconditional pseudorandom generators for low degree polynomials
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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
Breaking the ε-Soundness Bound of the Linearity Test over GF(2)
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
On the Approximation Resistance of a Random Predicate
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
3-bit dictator testing: 1 vs. 5/8
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
CSP gaps and reductions in the lasserre hierarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
Randomly supported independence and resistance
Proceedings of the forty-first annual ACM symposium on Theory of computing
Near-optimal algorithms for maximum constraint satisfaction problems
ACM Transactions on Algorithms (TALG)
ACM Transactions on Computation Theory (TOCT)
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
On the structure of cubic and quartic polynomials
Proceedings of the forty-second ACM symposium on Theory of computing
How to play unique games on expanders
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Breaking the $\epsilon$-Soundness Bound of the Linearity Test over GF(2)
SIAM Journal on Computing
Towards Sharp Inapproximability for Any 2-CSP
SIAM Journal on Computing
Pseudorandom Bits for Polynomials
SIAM Journal on Computing
Proceedings of the forty-third annual ACM symposium on Theory of computing
Randomly Supported Independence and Resistance
SIAM Journal on Computing
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Towards an optimal query efficient PCP?
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Approximation resistance on satisfiable instances for predicates with few accepting inputs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Majority is stablest: discrete and SoS
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Explicit Optimal Hardness via Gaussian Stability Results
ACM Transactions on Computation Theory (TOCT)
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We return to the study of the relation of query complexity and soundness in probabilistically checkable proofs.We present a PCP verifier for languages that are Unique-Games-Hard and such that the verifier makes q queries, has almost perfect completeness, and has soundness error at most 2q/2q+ε, for arbitrarily small ε0. For values of q of the form 2t-1, the soundness error is (q+1)/2q+ε.Charikar et al. show that there is a constant c such that for every language that has a verifier of query complexity q, and a ratio of soundness error to completeness smaller than cq/2q is decidable in polynomial time. Up to the value of the multiplicative constant and to the validity of the Unique Games Conjecture, our result is therefore tight.As a corollary, we show that approximating the Maximum Independent Set problem in graphs of degree Δ within a factor better than Δ/(log Δ)c is Unique-Games-Hard for a certain constant c0.Our main technical results are (i) a connection between the Gowers uniformity of a Boolean function and the influence of its variables and (ii) the proof that "Gowers uniform" functions pass the "hypergraph linearity test" approximately with the same probability of a random function. The connection between Gowers uniformity and influence might have other applications.