Title :
Pseudorandom generators, measure theory, and natural proofs
Author :
Regan, Kenneth W. ; Sivakumar, D. ; Cai, Jin-Yi
Author_Institution :
Dept. of Comput. Sci., State Univ. of New York, Buffalo, NY, USA
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
Keywords :
computational complexity; formal languages; random number generation; theorem proving; measure theory; natural proofs; partial converse; pseudorandom number generators; resource-bounded measure theory; Area measurement; Circuits; Complexity theory; Computer science; Natural languages; Polynomials; Size measurement; Terminology; Time measurement; Turing machines;
Conference_Titel :
Foundations of Computer Science, 1995. Proceedings., 36th Annual Symposium on
Conference_Location :
Milwaukee, WI
Print_ISBN :
0-8186-7183-1
DOI :
10.1109/SFCS.1995.492459