TY - GEN

T1 - A combinatorial consistency lemma with application to proving the PCP theorem

AU - Goldreich, Oded

AU - Safra, Shmuel

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1997.

PY - 1997

Y1 - 1997

N2 - The current proof of the PCP Theorem (i.e., NP=PCP (log, O(1))) is very complicated. One source of difficulty is the technically involved analysis of low-degree tests. Here, we refer to the difficulty of obtaining strong results regarding low-degree tests; namely, results of the type obtained and used by Arora and Safra and Arora et. al. In this paper, we eliminate the need to obtain such strong results on low-degree tests when proving the PCP Theorem. Although we do not get rid of low-degree tests altogether, using our results it is now possible to prove the PCP Theorem using a simpler analysis of low-degree tests (which yields weaker bounds). In other words, we replace the strong algebraic analysis of low-degree tests presented by Arora and Safra and Arora et. al. by a combinatorial lemma (which does not refer to low-degree tests or polynomials).

AB - The current proof of the PCP Theorem (i.e., NP=PCP (log, O(1))) is very complicated. One source of difficulty is the technically involved analysis of low-degree tests. Here, we refer to the difficulty of obtaining strong results regarding low-degree tests; namely, results of the type obtained and used by Arora and Safra and Arora et. al. In this paper, we eliminate the need to obtain such strong results on low-degree tests when proving the PCP Theorem. Although we do not get rid of low-degree tests altogether, using our results it is now possible to prove the PCP Theorem using a simpler analysis of low-degree tests (which yields weaker bounds). In other words, we replace the strong algebraic analysis of low-degree tests presented by Arora and Safra and Arora et. al. by a combinatorial lemma (which does not refer to low-degree tests or polynomials).

KW - Low-degree tests

KW - NP

KW - Parallelization of probabilistic proof systems

KW - Probabilistically checkable proofs (PCP)

UR - http://www.scopus.com/inward/record.url?scp=84957634883&partnerID=8YFLogxK

U2 - 10.1007/3-540-63248-4_7

DO - 10.1007/3-540-63248-4_7

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AN - SCOPUS:84957634883

SN - 3540632484

SN - 9783540632481

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 67

EP - 84

BT - Randomization and Approximation Techniques in Computer Science - International Workshop, RANDOM 1997, Proceedings

A2 - Rolim, José

PB - Springer Verlag

T2 - International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 1997

Y2 - 11 July 1997 through 12 July 1997

ER -