Simple PCPs with poly-log rate and query complexity

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2005, Pages 266-275

  Ben Sasson, Eli ^a,b   Sudan, Madhu ^c  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b TOYOTA TECHNOLOGICAL INSTITUTE AT CHICAGO   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Locally testable codes; PCP; PCPP; Probabilistically Checkable Proofs

Indexed keywords

LOCALLY TESTABLE CODES; PCPP; PROBABILISTICALLY CHECKABLE PROOFS (PCP); QUERY COMPLEXITY;

CIRCUIT THEORY; COMPUTATIONAL COMPLEXITY; POLYNOMIALS; QUERY LANGUAGES;

PROBABILISTIC LOGICS;

EID: 34848899251     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1060590.1060631     Document Type: Conference Paper

References (30)

1. ALON, N. Combinatorial Nullstellensatz. Combinatorics, Probability and Computing, 8 (1999), 7-29.
2. ARORA, S., LUND, C., MOTWANI, R., SUDAN, M., AND SZEGEDY, M. Proof verification and the hardness of approximation problems. Journal of the ACM 45, 3 (May 1998), 501-555.
3. ARORA, S., AND SAFRA, S. Probabilistic checking of proofs: A new characterization of NP. Journal of the ACM 45, 1 (Jan. 1998), 70-122.
4. BABAI, L., FORTNOW, L. AND LUND, C. Nondeterministic exponential time has two-prover interactive protocols Computational Complexity, 1(1):3-40, 1991.
5. BABAI, L., FORTNOW, L., LEVIN, L. A., AND SZEGEDY, M. Checking computations in polylogarithmic time. In Proc. 23rd ACM Symp. on Theory of Computing (New Orleans, Louisiana, 6-8 May 1991), pp. 21-31.
6. BARAK, B. How to go beyond the black-box simulation barrier. In Proc. 42nd IEEE Symp. on Foundations of Comp. Science (Las Vegas, Nevada, 14-17 Oct. 2001), pp. 106-115.
7. BELLARE, M., GODREICH, O., AND SUDAN, M. Free bits, PCPs, and nonapproximability - towards tight results. SIAM Journal of Computing 27, 3 (June 1998), 804-915.
8. BELLARE, M., GOLDWASSER, S., LUND, C., AND RUSSELL, A. Efficient probabilistically checkable proofs and applications to approximation. In Proc. 25th ACM Symp. on Theory of Computing (San Diego, California, 16-18 May 1993), pp. 294-304.
9. BEN-SASSON, E., GOLDREICH, O., HARSHA, P., SUDAN, M. AND VADHAN, S. Robust PCPs of Proximity, Shorter PCPs and Applications to Coding. In STOC 2004, Chicago.
10. BEN-SASSON, E. AND SUDAN, M. Simple PCPs with Poly-log Rate and Query Complexity. Preliminary version at http://eccc.uni-trier.de/eccc-reports/2004/TR04-060/index.html
11. BEN-SASSON, E., SUDAN, M., VADHAN, S., AND WIGDERSON, A. Randomness-efficient low degree tests and short PCPs via epsilon-biased sets. In Proc. 35th ACM Symp. on Theory of Computing (San Diego, California, 9-11 June 2003), pp. 612-621.
12. CANETTI, R., GOLDAEICH, O., AND HALEVI, S. The random oracle methodology, revisited. In Proc. 30th ACM Symp. on Theory of Computing (Dallas, Texas, 23-26 May 1998), pp. 209-218.
13. DINUR, I., FISCHER, E., KINDLER, G., RAZ, R., AND SAFRA, S. PCP Characterizations of NP: Towards a Polynomially-Small Error-Probability In Proc. 31st ACM Symp. on Theory of Computing, 1999, pp. 29-40
14. DINUR, I., AND REINGOLD, O. PCP testers: Towards a more combinatorial proof of PCP theorem. FOCS 2004.
15. FEIGE, U., GOLDWASSER, S., LOVÁSZ, L., SAFRA, S., AND SZEGEDY, M. Interactive proofs and the hardness of approximating cliques. Journal of the ACM 43, 2 (Mar. 1996), 268-293.
16. K. FRIEDL, Z. HATSAGI, AND A. SHEN. Low-degree tests. Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 57-64, 1994.
17. GOLDREICH, O. A sample of samplers - a computational perspective on sampling. Tech. Rep. TR97-020, Electronic Colloquium on Computational Complexity, 1997.O. GOLDREICH
18. GOLDREICH, O., AND SUDAN, M. Locally testable codes and PCPs of almost linear length. In Proc. 43rd IEEE Symp. on Foundations of Comp. Science (Vancouver, Canada, 16-19 Nov. 2002), pp. 13-22. (See ECC Report TR02-050, 2002).
19. GURUSWAMI, V., LEWIN, D., SUDAN, M., AND TREVISAN, L. A tight characterization of NP with 3-query PCPs. In Proc. 39th IEEE Symp. on Foundations of Comp. Science (Palo Alto, California, 8-11 Nov. 1998), pp. 18-27.
20. HARSHA, P., AND SUDAN, M. Small PCPs with low query complexity. Computational Complexity 9, 3-4 (Dec. 2000), 157-201.
21. HÁ̊STAD, J. Some optimal inapproximability results. Journal of the ACM 48, 4 (July 2001), 798-859.
22. KILIAN, J. A note on efficient zero-knowledge proofs and arguments (extended abstract). In Proc. 24th ACM Symp. on Theory of Computing (Victoria, British Columbia, Canada, 4-6 May 1992), pp. 723-732.
23. LIDL, R. AND NIEDERREITER, H Introduction to finite fields and their applications. Cambridge University Press, Cambridge, UK. Revised edition, 1994.
24. LINNIK, U. V. On the Least Prime in an Arithmetic Progression. I. The Basic Theorem. In Mat. Sbornik N. S. 15 (57), 139-178, 1944.
25. LUND, C., FORTNOW, L., KARLOFF, H., AND NISAN, N. Algebraic methods for interactive proof systems. In Proc. 31st IEEE Symp. on Foundations of Comp. Science (St. Louis, Missouri, 22-24 Oct. 1990), pp. 2-10.
26. MICALI, S. Computationally sound proofs. SIAM Journal of Computing 30, 4 (2000), 1253-1298.
27. POLISHCHUK, A., AND SPIELMAN, D. A. Nearly-linear size holographic proofs. In Proc. 26th ACM Symp. on Theory of Computing (Montréal, Québec, Canada, 23-25 May 1994), pp. 194-203.
28. RUBINFELD, R., AND SUDAN, M. Robust characterizations of polynomials with applications to program testing. SIAM Journal of Computing 25, 2 (Apr. 1996), 252-271. 1992).
29. SAMORODNITSKY, A., AND TREVISAN, L. A PCP characterization of NP with optimal amortized query complexity. In Proc. 32nd ACM Symp. on Theory of Computing (Portland, Oregon, 21-23 May 2000), pp. 191-199.
30. SPIELMAN, D. A. Computationally Efficient Error-Correcting Codes and Holographic Proofs Ph. D. Thesis, MIT, Cambridge, MA, 1995.