Small PCPs with Low Query Complexity

  • Prahladh Harsha
  • Madhu Sudan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2010)

Abstract

Most known constructions of probabilistically checkable proofs (PCPs) either blow up the proof size by a large polynomial, or have a high (though constant) query complexity. In this paper we give a transformation with slightly- super-cubic blowup in proof size, with a low query complexity. Specifically, the verifier probes the proof in 16 bits and rejects every proof of a false assertion with probability arbitrarily close to 1/2, while accepting corrects proofs of theo- rems with probability one. The proof is obtained by revisiting known construc- tions and improving numerous components therein. In the process we abstract a number of new modules that may be of use in other PCP constructions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Prahladh Harsha
    • 1
  • Madhu Sudan
    • 1
  1. 1.Laboratory for Computer ScienceMassachusetts Institute of TechnologyCambridgeUSA

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