Hardness vs. randomness

Abstract

A simple construction for a pseudorandom bit generator is presented. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (e.g. P, NC, PSPACE, etc.), using an arbitrary function that is hard for C. This generator reveals an equivalence between the problems of proving lower bounds and the problem of generating good pseudorandom sequences. Combining this construction with other arguments, a number of consequences are obtained.<>