Simplified derandomization of BPP using a hitting set generator

Authors:
Oded Goldreich;Salil Vadhan;Avi Wigderson
Affiliations:
Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, Israel;Computer Science and Applied Mathematics, Harvard School of Engineering Applied Sciences;School of Mathematics of the Institute, Princeton
Venue:
Studies in complexity and cryptography
Year:
2011

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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.