Abstract
A 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 RP = P, but it is not apparent what this implies for BPP. Nevertheless, Andreev et al. (ICALP'96, and JACM 1998) showed that a polynomial-time hitting-set generator implies the seemingly stronger conclusion BPP = P. We simplify and improve their (and later) constructions.
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