Short PCPPs verifiable in polylogarithmic time with O(1) queries

Annals of Mathematics and Artificial Intelligence

Volumn 56, Issue 3-4, 2009, Pages 313-338

  Mie, Thilo ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

PCP; PCPP; Query complexity; Time complexity; Verifier

Indexed keywords

EID: 77949773697     PISSN: 10122443     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10472-009-9169-y     Document Type: Article

References (15)

1. Arora, S., Barak, B.: Computational Complexity: A Modern Approach. Cambridge University Press, Cambridge (2009).
2. Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M.: Proof verification and hardness of approximation problems. J. ACM 45, 501-555 (1998).
3. Arora, S., Safra, S.: Probabilistic checking of proofs: a new characterisation of NP. J. ACM 45, 70-122 (1998).
4. Babai, L., Fortnow, L., Levin, L. A., Szegedy, M.: Checking computations in polylogarithmic time. In: STOC '91: Proceedings of the Twenty-third Annual ACM Symposium on Theory of Computing, pp. 21-32. ACM, New York (1991).
5. Barak, B., Goldreich, O.: Universal arguments and their applications. SIAM J. Comput. 38(5), 1661-1694 (2008).
6. Ben-Sasson, E., Goldreich, O., Harsha, P., Sudan, M., Vadhan, S.: Short PCPs verifiable in polylogarithmic time. In: CCC '05: Proceedings of the 20th Annual IEEE Conference on Computational Complexity, pp. 120-134. IEEE Computer Society, Washington, DC (2005).
7. Ben-Sasson, E., Sudan, M.: Short PCPs with polylog query complexity. SIAM J. Comput. 38(2), 551-607 (2008).
8. Dinur, I.: The PCP theorem by gap amplification. J. ACM 54(3) (2007).
9. Dinur, I., Reingold, O.: Assignment testers: towards a combinatorial proof of the PCP theorem. SIAM J. Comput. 36(4), 975-1024 (2006).
10. Feige, U., Goldwasser, S., Lovász, L., Safra, S., Szegedy, M.: Interactive proofs and the hardness of approximating cliques. J. ACM 43(2), 268-292 (1996).
11. Goldreich, O., Meir, O.: A small gap in the gap amplification of assignment testers. In: Comment 3 to TR05-046, Electronic Colloquium on Computational Complexity (2007).
12. Håstad, J.: Some optimal inapproximability results. J. ACM 48(4), 798-859 (2001).
13. Polishchuk, A., Spielman, D. A.: Nearly-linear Size Holographic Proofs, pp. 194-203. STOC (1994).
14. Reingold, O., Vadhan, S. P., Wigderson, A.: Entropy waves, the zig-zag graph product, and new constant-degree expanders and extractors. In: Electronic Colloquium on Computational Complexity (ECCC), vol. 8, no. 18 (2001).
15. Trevisan, L., Sorkin, G. B., Sudan, M., Williamson, D. P.: Gadgets, approximation, and linear programming. SIAM J. Comput. 29(6), 2074-2097 (2000).