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Pseudorandom generators, measure theory, and natural proofs

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3 Author(s)
K. W. Regan ; Dept. of Comput. Sci., State Univ. of New York, Buffalo, NY, USA ; D. Sivakumar ; Jin-Yi Cai

We prove that if strong pseudorandom number generators exist, then the class of languages that have polynomial-sized circuits (P/poly) is not measurable within exponential time, in terms of the resource-bounded measure theory of Lutz. We prove our result by showing that if P/poly has measure zero in exponential time, then there is a natural proof against P/poly, in the terminology of Razborov and Rudich (1994). We also provide a partial converse of this result

Published in:

Foundations of Computer Science, 1995. Proceedings., 36th Annual Symposium on

Date of Conference:

23-25 Oct 1995