Almost Transparent Short Proofs for NP

  • Klaus Meer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6914)


We study probabilistically checkable proofs (PCPs) in the real number model of computation as introduced by Blum, Shub, and Smale. Our main result is NP = PCP(O(logn), polylog(n)), i.e., each decision problem in NP is accepted by a verifier that generates O(logn) many random bits and reads polylog(n) many proof components. This is the first non-trivial characterization of NP by real PCP-classes. As a byproduct this result implies as well a characterization of real nondeterministic exponential time via NEXP = PCP(poly(n), poly(n)).


Polynomial System Univariate Polynomial Probabilistic Check Proof Logarithmic Number Real Number Model 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Klaus Meer
    • 1
  1. 1.Computer Science InstituteBTU CottbusCottbusGermany

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