Pseudorandom generators, measure theory, and natural proofs

Authors:
K. W. Regan;D. Sivakumar;Jin-Yi Cai
Affiliations:
-;-;-
Venue:
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Year:
1995

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Abstract

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.