Short PCPPs verifiable in polylogarithmic time with O(1) queries

  • Authors:

  • Thilo Mie

  • Affiliations:

  • Institut für Kryptographie und Sicherheit, Universität Karlsruhe (TH), Karlsruhe, Germany 76131

  • Venue:
  • Annals of Mathematics and Artificial Intelligence
  • Year:
  • 2009

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Abstract

In this paper we show for every pair language $L\subseteq \{0,1\}^*\times\{0,1\}^*$ in ${\ensuremath{\mathsf{NTIME}}}(T)$ for some non-decreasing function $T:{{\mathbb Z}}^+\rightarrow {{\mathbb Z}}^+$ there is a ${\ensuremath{\mathsf{PCPP}}}$ -verifier such that the following holds. In time poly (|x|,log|y|,logT(|x|驴+驴|y|)) it decides the membership of a purported word (x,y) by reading the explicit input x entirely and querying the implicit input y and the auxiliary proof of length T(|x|驴+驴|y|)·poly log T(|x|驴+驴|y|) in a constant number of positions.