Combinatorial PCPs with Efficient Verifiers

Research output: Contribution to journalArticlepeer-review


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., FOCS 1990), and a combinatorial construction of super-fast PCPs of Proximity for NP (first constructed by Ben-Sasson et al., CCC 2005).

Original languageEnglish
Pages (from-to)355-478
Number of pages124
JournalComputational Complexity
Issue number3
StatePublished - 1 Sep 2014
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014, Springer Basel.


  • PCP
  • PCP of Proximity
  • combinatorial
  • probabilistically checkable proofs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Mathematics
  • Computational Theory and Mathematics
  • Computational Mathematics


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  • Combinatorial PCPs with efficient verifiers

    Meir, O., 2009, Proceedings - 50th Annual Symposium on Foundations of Computer Science, FOCS 2009. p. 463-471 9 p. 5438606. (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS).

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

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