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Abstract: We show that a parallel repetition of any two-prover one-round proof system (MIP(2, 1)) decreases the probability of error at an exponential rate. No constructive bound was previously known. The constant in the exponent (in our analysis) depends only on the original probability of error and on the total number of possible answers of the two provers. The dependency on the total number of possible answers is logarithmic, which was recently proved to be almost the best possible [U. Feige and O.... (Update)
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BibTeX entry: (Update)
R. Raz. A Parallel Repetition Theorem. In 27th ACM Symposium on the Theory of Computing, pages 447--456, 1995. http://citeseer.ist.psu.edu/article/raz95parallel.html More
@inproceedings{ raz95parallel,
author = "Ran Raz",
title = "A parallel repetition theorem",
pages = "447--456",
year = "1995",
url = "citeseer.ist.psu.edu/article/raz95parallel.html" }
Citations (may not include all citations):403 Proof Verification and Hardness of Approximation Problems - ARORA - 1994
300 the hardness of approximating minimization problems (context) - LUND, YANNAKAKIS - 1993
242 Non-deterministic exponential time has two-prover interactiv.. - BABAI, FORTNOW et al. - 1990
212 Probabilistic checking of proofs: A new characterization of .. - ARORA, SAFRA - 1992
203 Approximating clique is almost NP-complete (context) - FEIGE, GOLDWASSER et al. - 1991
197 Cambridge University Press (context) - KUSHILEVITZ, NISAN et al. - 1997
173 Proof verification and intractability of approximation probl.. (context) - ARORA, LUND et al. - 1992
118 A parallel repetition theorem - RAZ - 1995
108 Improved non-approximability results - BELLARE, SUDAN - 1994
108 Hardness of approximations - ARORA, LUND - 1996
93 the power of multi-prover interactive protocols - FORTNOW, ROMPEL et al. - 1990
93 the power of multi-prover interactive protocols - FORTNOW, ROMPEL et al. - 1988
83 Multi prover interactive proofs: How to remove intractabilit.. (context) - BEN-OR, GOLDWASSER et al. - 1988
69 Some optimal inapproximability results (context) - ASTAD - 1997
68 Entropy and Information Theory - GRAY - 1990
66 Information Theory: Coding Theorems for Discrete Memoryless .. (context) - CSISZAR, KORNER - 1981
57 The probabilistic communication complexity of set intersecti.. (context) - KALYANASUNDARAM, SCHNITGER - 1987
50 the distributional complexity of disjointness (context) - RAZBOROV - 1992
49 Fully parallelized multi prover protocols for NEXP-time (context) - LAPIDOT, SHAMIR - 1991
36 The complexity of approximating a nonlinear program - BELLARE, ROGAWAY - 1995
24 and nonapproximability--- towards tight results (context) - BELLARE, GOLDREICH et al. - 1998
17 PSPACE is provable by two provers in one round - CAI, CONDON et al. - 1994
16 Impossibility results for recycling random bits in two prove.. (context) - FEIGE, KILIAN - 1995
14 Complexity-Theoretic Aspects of Interactive Proof Systems - FORTNOW - 1989
14 the success probability of the two provers in one round proo.. (context) - FEIGE - 1991
11 Testing of the long code and hardness for clique (context) - ASTAD - 1996
11 Towards the parallel repetition conjecture (context) - VERBITSKY - 1996
10 On bounded round multi-prover interactive proof systems (context) - CAI, CONDON et al. - 1990
8 Two prover protocols: Low error at a#ordable rates (context) - FEIGE, KILIAN - 1994
7 Probabilistic methods in extremal finite set theory (context) - ALON - 1994
6 Error reduction by parallel repetition: A negative result (context) - FEIGE, VERBITSKY - 1996
6 Strong Separation Models of Multi Prover Interactive Proofs (context) - KILIAN - 1990
5 Error Reduction by Parallel Repetition: The State of the Art - FEIGE
5 Interactive proofs and approximation (context) - BELLARE - 1993
5 Playing games of incomplete information (context) - CAI, CONDON et al. - 1992
4 The Parallel Repetition Conjecture for Trees is True (context) - VERBITSKY - 1994
4 Clique is Hard to Approximate Within n (context) - ASTAD - 1996
3 Two-prover one-round proof systems (context) - FEIGE, LOVASZ - 1992
3 cient probabilistic checkable proofs and applications to app.. (context) - BELLARE, GOLDWASSER et al. - 1993
3 prover zero-knowledge proofs for NP (context) - DWORK, FEIGE et al. - 1992
2 zero-knowledge protocol for NP (context) - LAPIDOT, SHAMIR et al. - 1995
2 and three-prover proof systems (context) - TARDOS, schemes - 1996
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