A PCP characterization of NP with optimal amortized query complexity

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2000, Pages 191-199

  Samorodnitsky, Alex ^a   Trevisan, Luca ^b  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b Och Spine at New York Presbyterian Hospitals   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIT COMPLEXITY; LINEARITY TESTING; LOWER BOUNDS; LOWER ORDER TERMS; MAXIMUM CLIQUE PROBLEMS; NON-APPROXIMABILITY; QUERY COMPLEXITY; TESTING ALGORITHM; AMORTIZED QUERY COMPLEXITY; LINEARITY TESTING ALGORITHMS;

ALGORITHMS; CHARACTERIZATION; COMPUTATIONAL COMPLEXITY; OPTIMIZATION; APPROXIMATION THEORY; CONSTRAINT THEORY; ERROR CORRECTION; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS; QUERY LANGUAGES; THEOREM PROVING;

CONSTRAINT SATISFACTION PROBLEMS; COMPUTATIONAL COMPLEXITY;

EID: 0033718183     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/335305.335329     Document Type: Conference Paper

References (25)

1. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and hardness of approximation problems. Journal of the ACM, 45(3):501-555, 1998. Preliminary version in Proc. of FOCS'92.
2. S. Arora and S. Safra. Probabilistic checking of proofs: A new characterization of NP. Journal of the ACM, 45(1):70-122, 1998. Preliminary version in Proc. of FOCS'92.
3. S. Arora and M. Sudan. Improved low degree testing and its applications. In Proceedings of the 29th ACM Symposium on Theory of Computing, pages 485-495, 1997.
4. M. Bellare. Proof checking and approximation: Towards tight results. Sigact News, 27(1), 1996.
5. M. Bellare, O. Goldreich, and M. Sudan. Free bits, PCP's and non-approximability - towards tight results. SIAM Journal on Computing, 27(3):804-915, 1998. Preliminary version in Proc. of FOCS'95.
6. M. Bellare, S. Goldwasser, C. Lund, and A. Russell. Efficient probabilistically checkable proofs and applications to approximation. In Proceedings of the 25th ACM Symposium on Theory of Computing, pages 294-304, 1993. See also the errata sheet in Proc of STOC'94.
7. M. Bellare and M. Sudan. Improved non-approximability results. In Proceedings of the 26th ACM Symposium on Theory of Computing, pages 184-193, 1994.
8. M. Blum, M. Luby, and R. Rubinfeld. Self-testing/correcting with applications to numerical problems. In Proceedings of the 22nd ACM Symposium on Theory of Computing, pages 73-83, 1990.
9. N. Creignou. A dichotomy theorem for maximum generalized satisfiability problems. Journal of Computer and System Sciences, 51(3):511-522, 1995.
10. I. Dinur, E. Fischer, G. Kindler, R. Raz, and S. Safra. PCP characterizations of NP: Towards a polynomially-small error-probability. In Proceedings of the 31st ACM Symposium on Theory of Computing, pages 29-40, 1999.
11. U. Feige, S. Goldwasser, L. Lovász, S. Safra, and M. Szegedy. Approximating clique is almost NP-complete. In Proceedings of the 32nd IEEE Symposium on Foundations of Computer Science, pages 2-12, 1991.
12. U. Feige and J. Kilian. Two prover protocols - low error at affordable rates. In Proceedings of the 26th ACM Symposium on Theory of Computing, pages 172-183, 1994.
13. 1-ε. In Proceedings of the 37th IEEE Symposium on Foundations of Computer Science, pages 627-636, 1996.
14. J. H̊stad. Some optimal inapproximability results. In Proceedings of the 29th ACM Symposium on Theory of Computing, pages 1-10, 1997.
15. S. Khanna, R. Motwani, M. Sudan, and U. Vazirani. On syntactic versus computational views of approximability. SIAM Journal on Computing, 28(1):164-191, 1999. Preliminary version in Proe. of FOCS'94.
16. S. Khanna, M. Sudan, and D. Williamson. A complete classification of the approximability of maximization problems derived from boolean constraint satisfaction. In Proceedings of the 29th ACM Symposium on Theory of Computing, pages 11-20, 1997.
17. R. Raz and S. Safra. A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP. In Proceedings of the 29th ACM Symposium on Theory of Computing, pages 475-484, 1997.
18. M. Serna, L. Trevisan, and F. Xhafa. The parallel approximability of non-boolean constraint satisfaction and restricted integer linear programming. In Proceedings of the 15th Symposium on Theoretical Aspects of Computer Science, pages 488-498. LNCS 1373, Springer-Verlag, 1998.
19. M. Sudan and L. Trevisan. Probabilistically checkable proofs with low amortized query complexity. In Proceedings of the 39th IEEE Symposium on Foundations of Computer Science, 1998.
20. L. Trevisan. Positive linear programming, parallel approximation, and PCP's. In Proceedings of the 4th European Symposium on Algorithms, pages 62-75. LNCS 1136, Springer-Verlag, 1996.
21. L. Trevisan. Approximating satisfiable satisfiability problems. In Proceedings of the 5th European Symposium on Algorithms, pages 472-485. LNCS 1284, Springer-Verlag, 1997.
22. L. Trevisan. Recycling queries in PCPs and in linearity tests. In Proceedings of the 30th ACM Symposium on Theory of Computing, 1998.
23. L. Trevisan, G. Sorkin, M. Sudan, and D. Williamson. Gadgets, approximation, and linear programming. In Proceedings of the 37th IEEE Symposium on Foundations of Computer Science, pages 617-626, 1996.
24. U. Zwick. Approximation algorithms for constraint satisfaction problems involving at most three variables per constraint. In Proceedings of the 9th ACM-SIAM Symposium on Discrete Algorithms, 1998.
25. U. Zwick. Finding almost satisfying assignment. In Proceedings of the 30th ACM Symposium on Theory of Computing, 1998.