Derandomized parallel repetition of structured PCPs

Irit Dinur, Or Meir

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


A PCP is a proof system for NP in which the proof can be checked by a probabilistic verifier. The verifier is only allowed to read a very small portion of the proof, and in return is allowed to err with some bounded probability. The probability that the verifier accepts a false proof is called the soundness error, and is an important parameter of a PCP system that one seeks to minimize. Constructing PCPs with sub-constant soundness error and, at the same time, a minimal number of queries into the proof (namely two) is especially important due to applications for inapproximability. In this work we construct such PCP verifiers, i.e., PCPs that make only two queries and have sub-constant soundness error. Our construction can be viewed as a combinatorial alternative to the "manifold vs. point" construction, which is the only construction in the literature for this parameter range. The "manifold vs. point" PCP is based on a low degree test, while our construction is based on a direct product test. Our construction of a PCP is based on extending the derandomized direct product test of Impagliazzo, Kabanets and Wigderson (STOC 09) to a derandomized parallel repetition theorem. More accurately, our PCP construction is obtained in two steps. We first prove a derandomized parallel repetition theorem for specially structured PCPs. Then, we show that any PCP can be transformed into one that has the required structure, by embedding it on a de-Bruijn graph.

Original languageEnglish
Title of host publicationProceedings - 25th Annual IEEE Conference on Computational Complexity, CCC 2010
Number of pages12
StatePublished - 2010
Externally publishedYes
Event25th Annual IEEE Conference on Computational Complexity, CCC 2010 - Cambridge, MA, United States
Duration: 9 Jun 201011 Jun 2010

Publication series

NameProceedings of the Annual IEEE Conference on Computational Complexity
ISSN (Print)1093-0159


Conference25th Annual IEEE Conference on Computational Complexity, CCC 2010
Country/TerritoryUnited States
CityCambridge, MA


  • De-Bruijn
  • Derandomized parallel repetition
  • Direct product
  • Direct product test
  • Low error
  • PCP

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Computational Mathematics


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