A combinatorial consistency lemma with application to proving the PCP theorem

Oded Goldreich, Shmuel Safra

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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).

Original languageEnglish
Title of host publicationRandomization and Approximation Techniques in Computer Science - International Workshop, RANDOM 1997, Proceedings
EditorsJosé Rolim
PublisherSpringer Verlag
Pages67-84
Number of pages18
ISBN (Print)3540632484, 9783540632481
DOIs
StatePublished - 1997
EventInternational Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 1997 - Bologna, Italy
Duration: 11 Jul 199712 Jul 1997

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1269
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceInternational Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 1997
Country/TerritoryItaly
CityBologna
Period11/07/9712/07/97

Keywords

  • Low-degree tests
  • NP
  • Parallelization of probabilistic proof systems
  • Probabilistically checkable proofs (PCP)

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