PCPs with small soundness error

Authors:
Irit Dinur
Affiliations:
Weizmann Institute of Science, Rehovot, Israel
Venue:
ACM SIGACT News
Year:
2008

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Abstract

The soundness error of a PCP verifier is the probability (usually denoted ε) that the verifier accepts an incorrect input. We are interested in the smallest possible values of ε for which the PCP theorem holds, and in particular whether the theorem holds when ε is an inverse polynomial function of the input length. We discuss the 'sliding scale conjecture' of [BGLR93, LY94] and related questions. We then sketch some of the existing approaches and constructions of PCPs with sub-constant soundness error.