Sound 3-Query PCPPs Are Long

  • Eli Ben-Sasson
  • Prahladh Harsha
  • Oded Lachish
  • Arie Matsliah
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5125)

Abstract

We initiate the study of the tradeoff between the length of a probabilistically checkable proof of proximity (PCPP) and the maximal soundness that can be guaranteed by a 3-query verifier with oracle access to the proof. Our main observation is that a verifier limited to querying a short proof cannot obtain the same soundness as that obtained by a verifier querying a long proof. Moreover, we quantify the soundness deficiency as a function of the proof-length and show that any verifier obtaining “best possible” soundness must query an exponentially long proof.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Eli Ben-Sasson
    • 1
  • Prahladh Harsha
    • 2
  • Oded Lachish
    • 3
  • Arie Matsliah
    • 1
  1. 1.Computer Science DepartmentTechnion, Israel Institute of TechnologyHaifaIsrael
  2. 2.Toyota Technological InstituteChicagoUSA
  3. 3.Centre for Discrete Mathematics and its Applications (DIMAP)University of WarwickCoventryUnited Kingdom

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