computational complexity

, Volume 9, Issue 3–4, pp 157–201 | Cite as

Small PCPs with low query complexity

  • P. Harsha
  • M. Sudan

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 correct proofs of theorems with probability one. The proof is obtained by revisiting known constructions and improving numerous components therein. In the process we abstract a number of new modules that may be of use in other PCP constructions.

Keywords. NP completeness, probabilistic proof systems, holographic proofs. 

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Copyright information

© Birkhäuser Verlag, Basel 2000

Authors and Affiliations

  • P. Harsha
    • 1
  • M. Sudan
    • 2
  1. 1.Laboratory for Computer Science, Massachusetts Institute of Technology, 545 Technology Square, Cambridge, MA 02139, U.S.A., e-mail: prahladh@mit.eduUS
  2. 2.Laboratory for Computer Science, Massachusetts Institute of Technology, 545 Technology Square, Cambridge, MA 02139, U.S.A., e-mail: madhu@mit.edu, http://theory.lcs.mit.edu/~madhu/US

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