Simplified Derandomization of BPP Using a Hitting Set Generator

Abstract

AbstractA hitting-set generator is a deterministic algorithm that generates a set of strings such that this set intersects every dense set that is recognizable by a small circuit. A polynomial time hitting-set generator readily implies \(\mathcal{RP}=\mathcal{P}\), but it is not apparent what this implies for \(\mathcal{BPP}\). Nevertheless, Andreev et al. (ICALP’96, and JACM 1998) showed that a polynomial-time hitting-set generator implies the seemingly stronger conclusion \(\mathcal{BPP=P}\). We simplify and improve their (and later) constructions.KeywordsDerandomizationRPBPPone-sided error versus two-sided error