Randomness is linear in space

Abstract

We show that any randomized algorithm that runs in space S and time T and uses poly(S) random bits can be simulated using only O(S) random bits in space S and time T+poly(S). A deterministic simulation in space S follows. Of independent interest is our main technical tool: a procedure which extracts randomness from a defective random source using a small additional number of truly random bits. © 1996 Academic Press, Inc.