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 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
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
A 3-Query Non-Adaptive PCP with Perfect Completeness
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Low-degree tests at large distances
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
Structure and Randomness in Combinatorics
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
3-bit dictator testing: 1 vs. 5/8
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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
Conditional Hardness for Approximate Coloring
SIAM Journal on Computing
More efficient queries in PCPs for NP and improved approximation hardness of maximum CSP
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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The problem of dictatorship testing is often used a starting in constructing a PCP system. Samorodnitsky and Trevisan in STOC 2006 designed a dictatorship test that makes q queries and has soundness approximately O(qċ2-q). However, their test has imperfect completeness. We describe some of the progress made in designing dictatorship tests with perfect completeness.