We construct a PCP for NTIME(2n) with constant soundness, 2 n poly(n) proof length, and poly(n) queries where the verifier's computation is simple: the queries are a projection of the input randomness, and the computation on the prover's answers is a 3CNF. The previous upper bound for these two computations was polynomial-size circuits. Composing this verifier with a proof oracle increases the circuit-depth of the latter by 2. Our PCP is a simple variant of the PCP by Ben-Sasson, Goldreich, Harsha, Sudan, and Vadhan (CCC 2005). We also give a more modular exposition of the latter, separating the combinatorial from the algebraic arguments. If our PCP is taken as a black box, we obtain a more direct proof of the result by Williams, later with Santhanam (CCC 2013) that derandomizing circuits on n bits from a class C in time 2 n /nω(1) yields that NEXP is not in a related circuit class C′ Our proof yields a tighter connection: C is an And-Or of circuits from C′. Along the way we show that the same lower bound follows if the satisfiability of the And of any 3 circuits from C′ can be solved in time 2n/nω(1). © 2014 Springer-Verlag.
CITATION STYLE
Ben-Sasson, E., & Viola, E. (2014). Short PCPs with projection queries. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8572 LNCS, pp. 163–173). Springer Verlag. https://doi.org/10.1007/978-3-662-43948-7_14
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