Simplified derandomization of BPP using a hitting set generator

A hitting-set generator is a deterministic algorithm which generates a set of strings that intersects every dense set recognizable by a small circuit. A polynomial time hitting-set generator readily implies RP = P . Andreev et. al. (ICALP'96, and JACM 1998) showed that if polynomial-time hitting-set generator in fact implies the much stronger conclusion BPP = P . We simplify and improve their (and later) constructions. Keywords: Derandomization, RP, BPP , one-sided error versus two-sided error A preliminary version of this work has appeared in the proceedings of Random99. y Department of Computer Science, Weizmann Institute of Science, Rehovot, Israel. [email protected]. z MIT Laboratory for Computer Science, 545 Technology Square, Cambridge, MA 02139. [email protected]. Supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship. x Institute of Computer Science, The Hebrew University of Jerusalem, Givat-Ram, Jerusalem, Israel. [email protected]...

Simplified derandomization of BPP using a hitting set generator

A hitting-set generator is a deterministic algorithm which generates a set of strings that intersects every dense set recognizable by a small circuit. A polynomial time hitting-set generator readily implies RP = P . Andreev et. al. (ICALP'96, and JACM 1998) showed that if polynomial-time hitting-set generator in fact implies the much stronger conclusion BPP = P . We simplify and improve their (and later) constructions. Keywords: Derandomization, RP, BPP , one-sided error versus two-sided error A preliminary version of this work has appeared in the proceedings of Random99. y Department of Computer Science, Weizmann Institute of Science, Rehovot, Israel. [email protected]. z MIT Laboratory for Computer Science, 545 Technology Square, Cambridge, MA 02139. [email protected]. Supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship. x Institute of Computer Science, The Hebrew University of Jerusalem, Givat-Ram, Jerusalem, Israel. [email protected]...

Simplified derandomization of BPP using a hitting set generator \Lambda

Abstract A hitting-set generator is a deterministic algorithm which generates a set of strings that intersects every dense set recognizable by a small circuit. A polynomial time hitting-set generator readily implies RP = P. Andreev et. al. (ICALP'96, and JACM 1998) showed that if polynomial-time hitting-set generator in fact implies the much stronger conclusion BPP = P. We simplify and improve their (and later) constructions