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Abstract: This paper strengthens the low-error PCP characterization of NP, coming closer to the ultimate BGLR conjecture. Namely, we prove that witnesses for membership in any NP language can be verified with a constant number of accesses, and with an error probability exponentially small in the number of bits accessed, as long as this number is at most (log n) for any constant fi ! 1. (Compare with the BGLR conjecture, claiming the same for any fi 1). (Update)
Context of citations to this paper: More
...purpose, any of the known PCP theorems would do, since the only property we need is a constant error probability. Theorem 3 (PCP Theorem [8]) Let Phi = fOE 1 ; OE ng be a system of tests over variables V = fx 1 ; xn 0 g such that each test depends on O(1) variables,...
.... the role of the curves of [1] We note that Dinur et al. also use higher dimensional varieties in the proof of PCP related theorems [7]. Their use of varieties is for purposes quite different from ours. We are now ready to describe the MIP verifier for GapPCS ffl;m;b;q ....
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BibTeX entry: (Update)
Dinur, Fischer, Kindler, Raz, and Safra. PCP characterizations of NP: Towards a polynomially-small error-probability. In STOC: ACM Symposium on Theory of Computing (STOC), 1999. http://citeseer.ist.psu.edu/dinur98pcp.html More
@inproceedings{ dinur99pcp,
author = "Irit Dinur and Eldar Fischer and Guy Kindler and Ran Raz and Shmuel Safra",
title = "{PCP} characterizations of {NP}: towards a polynomially-small error-probability",
pages = "29--40",
year = "1999",
url = "citeseer.ist.psu.edu/dinur98pcp.html" }
Citations (may not include all citations):300 the hardness of approximating minimization problems (context) - Lund, Yannakakis - 1994
242 Non-deterministic exponential time has two-prover interactiv.. - Babai, Fortnow et al. - 1991
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203 Approximating clique is almost NPcomplete (context) - Feige, Goldwasser et al. - 1991
173 Proof verification and intractability of approximation probl.. (context) - Arora, Lund et al. - 1992
118 A parallel repetition theorem - Raz - 1998
95 A sub-constant error-probability low-degree test - Raz, Safra - 1997
82 Improved low degree testing and its applications - Arora, Sudan - 1997
69 Two-prover one-round proof systems: Their power and their pr.. (context) - Feige, Lovasz - 1992
49 Fully parallelized multi prover protocols for NEXPTIME (context) - Lapidot, Shamir - 1991
27 Some optimal inapproximability results - Hastad - 1997
24 and nonapproximability--- towards tight results (context) - Bellare, Goldreich et al. - 1998
18 Efficient multi-prover interactive proofs with applications .. (context) - Bellare, Goldwasser et al. - 1993
15 A well-characterized approximation problem - Hastad, Phillips et al. - 1993
13 Minimum propositional proof length is NP-hard to linearly ap.. - Alekhnovich, Buss et al. - 1998
2 Monotone-minimum-satisfying assignment is NP-hard for almost.. (context) - Dinur, Safra - 1998
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