Pseudorandom Generators, Measure Theory, and Natural Proofs

We prove that if strong pseudorandom number generators exist, then the class of languages that have polynomialsized circuits (P/poly) is not measurable within exponential time, in terms of the resource-bounded measure theory of Lutz. We prove our result by showingthat if P/polyhas measure zero in exponential time, then there is a natural proof against P/poly, in the terminology of Razborov and Rudich [25]. We also provide a partial converse of this result.

• Type: Conference
• Year: 1995
• Where: FOCS
• Authors: Kenneth W. Regan, D. Sivakumar, Jin-yi Cai
• Keywords: Exponential Time, FOCS 1995, Pseudorandom Number Generators, Resource-bounded Measure Theory, Theoretical Computer Science