Explicit OR-dispersers with polylogarithmic degree
Journal of the ACM (JACM)
A new general derandomization method
Journal of the ACM (JACM)
Construction of extractors using pseudo-random generators (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
SAGA '01 Proceedings of the International Symposium on Stochastic Algorithms: Foundations and Applications
Derandomizing Arthur-Merlin Games Using Hitting Sets
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Near-Optimal Conversion of Hardness into Pseudo-Randomness
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Pseudo-random generators for all hardnesses
Journal of Computer and System Sciences - STOC 2002
Derandomizing Arthur-Merlin games using hitting sets
Computational Complexity
One-sided versus two-sided error in probabilistic computation
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Simplified derandomization of BPP using a hitting set generator
Studies in complexity and cryptography
Computational complexity since 1980
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
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We show how to simulate any BPP algorithm in polynomial time using a weak random source of min-entropy r/sup /spl gamma// for any /spl gamma/0. This follows from a more general result about sampling with weak random sources. Our result matches an information-theoretic lower bound and solves a question that has been open for some years. The previous best results were a polynomial time simulation of RP (Saks et al., 1995) and a n(log/sup (k)/n)-time simulation of BPP for fixed k (Ta-Shma, 1996). Departing significantly from previous related works, we do not use extractors; instead we use the OR-disperser of (Saks et al., 1995) in combination with a tricky use of hitting sets borrowed from Andreev et al. (1996). Of independent interest is our new (simplified) proof of the main result of Andreev et al., (1996). Our proof also gives some new hardness/randomness trade-offs for parallel classes.