Improved 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.

[1]  Luca Trevisan,et al.  Construction of extractors using pseudo-random generators (extended abstract) , 1999, STOC '99.

[2]  Oded Goldreich,et al.  Another proof that BPP subseteq PH (and more) , 1997, Electron. Colloquium Comput. Complex..

[3]  Clemens Lautemann,et al.  BPP and the Polynomial Hierarchy , 1983, Inf. Process. Lett..

[4]  José D. P. Rolim,et al.  A new general derandomization method , 1998, JACM.

[5]  Leonard M. Adleman,et al.  Two theorems on random polynomial time , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[6]  Oded Goldreich,et al.  Another proof that bpp?ph (and more) , 1997 .

[7]  Avi Wigderson,et al.  P = BPP if E requires exponential circuits: derandomizing the XOR lemma , 1997, STOC '97.

[8]  Yacov Yacobi,et al.  The Complexity of Promise Problems with Applications to Public-Key Cryptography , 1984, Inf. Control..

[9]  José D. P. Rolim,et al.  Weak random sources, hitting sets, and BPP simulations , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[10]  Lance Fortnow,et al.  One-sided Versus Two-sided Randomness , 1998 .

[11]  Ran Raz,et al.  Extracting all the randomness and reducing the error in Trevisan's extractors , 1999, STOC '99.

[12]  Michael Sipser,et al.  A complexity theoretic approach to randomness , 1983, STOC.

[13]  Luca Trevisan,et al.  Constructions of Near-Optimal Extractors Using Pseudo-Random Generators , 1998, Electron. Colloquium Comput. Complex..