Combinatorial PCPs with efficient verifiers

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

Abstract

The PCP theorem asserts the existence of proofs that can be verified by a verifier that reads only a very small part of the proof. The theorem was originally proved by Arora and Safra (J. ACM 45(1)) and Arora et al. (J. ACM 45(3)) using sophisticated algebraic tools. More than a decade later, Dinur (J. ACM 54(3)) gave a simpler and arguably more intuitive proof using alternative combinatorial techniques. One disadvantage of Dinur's proof compared to the previous algebraic proof is that it yields less efficient verifiers. In this work, we provide a combinatorial construction of PCPs with verifiers that are as efficient as the ones obtained by the algebraic methods. The result is the first combinatorial proof of the PCP theorem for NEXP (originally proved by Babai et al., STOC 1991), and a combinatorial construction of super-fast PCPs of Proximity for NP (first constructed by Ben-Sasson et al., CCC 2005).

Original languageEnglish
Title of host publicationProceedings - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009
Pages463-471
Number of pages9
DOIs
StatePublished - 2009
Externally publishedYes
Event50th Annual Symposium on Foundations of Computer Science, FOCS 2009 - Atlanta, GA, United States
Duration: 25 Oct 200927 Oct 2009

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428

Conference

Conference50th Annual Symposium on Foundations of Computer Science, FOCS 2009
Country/TerritoryUnited States
CityAtlanta, GA
Period25/10/0927/10/09

ASJC Scopus subject areas

  • General Computer Science

Cite this