Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Inapproximability results for set splitting and satisfiability problems with no mixed clauses
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Approximation algorithms for MAX-3-CUT and other problems via complex semidefinite programming
Journal of Computer and System Sciences - STOC 2001
Robust pcps of proximity, shorter pcps and applications to coding
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Simple PCPs with poly-log rate and query complexity
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Every 2-CSP allows nontrivial approximation
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Probabilistic Proof Systems: A Primer
Foundations and Trends® in Theoretical Computer Science
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
Randomly supported independence and resistance
Proceedings of the forty-first annual ACM symposium on Theory of computing
ACM Transactions on Computation Theory (TOCT)
Improved Inapproximability Results for Maximum k-Colorable Subgraph
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
A query efficient non-adaptive long code test with perfect completeness
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on 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
Randomly Supported Independence and Resistance
SIAM Journal on Computing
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
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
Combinatorial approximation algorithms: a comparative review
Operations Research Letters
A characterization of approximation resistance for even k-partite CSPs
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
On the power of many one-bit provers
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
On the usefulness of predicates
ACM Transactions on Computation Theory (TOCT)
New NP-Hardness Results for 3-Coloring and 2-to-1 Label Cover
ACM Transactions on Computation Theory (TOCT)
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It is known that there exists a PCP characterization of NP where the verifier makes 3 queries and has a one-sided error that is bounded away from 1; and also that 2 queries do not suffice for such a characterization. Thus PCPs with 3 queries possess non-trivial verification power and motivate the task of determining the lowest error that can be achieved with a 3-query PCP. Recently, Hastad [STOC '97] has shown a tight characterization of NP by constructing a 3-query PCP verifier with ``error'' arbitrarily close to 1/2. Unfortunately, this verifier makes two-sided error and Hastad makes essential use of this feature. One-sided error, on the other hand, is a natural notion to associate with a proof system, since it has the desirable property that every rejected proof has a short counterexample. The question of determining the smallest error for which there exists a 3-query PCP verifier making one-sided error and accepting an NP-complete language, however, remained open.We resolve this question by showing that NP has a 3-query PCP with a one-sided error that is arbitrarily close to 1/2. This characterization is tight, i.e., the error cannot be lower. This result is in seeming contradiction with the results of Trevisan [ESA'97] and Zwick [SODA '98] who show that in order to recognize an NP-complete language, the error probability of a PCP verifier making 3 "non-adaptive" queries and having one-sided error must be at least 5/8. We get around this bottleneck by designing an "adaptive" 3-query PCP for NP. Our result yields the first tight analysis of an adaptive PCP; and reveals a previously unsuspected separation between the powers of adaptive and non-adaptive PCPs.Our design and analysis of adaptive PCPs can be extended to higher number of queries as well and we give an example of such a proof system with 5 queries. Our adaptive verifiers yield proof systems whose error probabilities match those of previous constructions, while also achieving one-sidedness in the error. This raises new questions about the power of adaptive PCPs, which deserve further study.