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| + |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| + |y|)·poly log T(|x| + |y|) in a constant number of positions.
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Mie, T. Short PCPPs verifiable in polylogarithmic time with O(1) queries. Ann Math Artif Intell 56, 313–338 (2009). https://doi.org/10.1007/s10472-009-9169-y
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DOI: https://doi.org/10.1007/s10472-009-9169-y