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)
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
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)
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
Testing Basic Boolean Formulae
SIAM Journal on Discrete Mathematics
Simple analysis of graph tests for linearity and PCP
Random Structures & Algorithms
A Tight Characterization of NP with 3 Query PCPs
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Probabilistically Checkable Proofs with Low Amortized Query Complexity
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Guest column: inapproximability results via Long Code based PCPs
ACM SIGACT News
Some 3CNF Properties Are Hard to Test
SIAM Journal on Computing
A 3-Query Non-Adaptive PCP with Perfect Completeness
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Testing for Concise Representations
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
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
Improved Bounds for Testing Juntas
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
Property Testing
Testing juntas nearly optimally
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
Conditional hardness for satisfiable 3-CSPs
Proceedings of the forty-first annual ACM symposium on Theory of computing
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
Gowers Uniformity, Influence of Variables, and PCPs
SIAM Journal on Computing
Linearity testing in characteristic two
IEEE Transactions on Information Theory - Part 1
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Long Code testing is a fundamental problem in the area of property testing and hardness of approximation. Long Code is a function of the form f(x) = xi for some index i. In the Long Code testing, the problem is, given oracle access to a collection of Boolean functions, to decide whether all the functions are the same Long Code, or cross-influences of any two functions are small. In this paper, we study the following problem: How small the soundness s of the Long Code test with perfect completeness can be by using non-adaptive q queries? We give a Long Code test with s = (2q+3)/2q, where q is of the form 2k-1 for any integer k 2. Our test is a "noisy" version of Samorodnitsky-Trevisan's Hyper Graph linearity test with suitably chosen noise distribution. To bound the soundness, we use Invariance-Principle style analysis in the spirit of O'Donnell and Wu (STOC 2009). Previously, Håstad and Khot (Theory of Computing, 2005) had shown s = 24√q/2q for infinitely many q. Chen (RANDOM 2009) improved this to s = q3/2q for infinitely many q with "adaptive" queries. As for the Long Code test with "almost" perfect completeness, Samorodnitsky and Trevisan (SICOMP, 2009) have shown s = 2q/2q (or even (q + 1)/2q for infinitely many q). Austrin and Mossel (Computational Complexity, 2009) have improved this to s = (q+o(q))/2q (or even (q+4)/2q assuming the famous Hadamard Conjecture) for any q.