How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
The complexity of Boolean functions
The complexity of Boolean functions
Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
Using hard problems to create pseudorandom generators
Using hard problems to create pseudorandom generators
Journal of Computer and System Sciences
Randomized algorithms
On extracting randomness from weak random sources (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Explicit OR-dispersers with polylogarithmic degree
Journal of the ACM (JACM)
Worst-Case Hardness Suffices for Derandomization: A New Method for Hardness-Randomness Trade-Offs
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Efficient Construction of Hitting Sets for Systems of Linear Functions
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Extracting Randomness: How and Why - A survey
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Weak random sources, hitting sets, and BPP simulations
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Explicit OR-dispersers with polylogarithmic degree
Journal of the ACM (JACM)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Extractors and pseudorandom generators
Journal of the ACM (JACM)
Pseudo-random generators for all hardnesses
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
In search of an easy witness: exponential time vs. probabilistic polynomial time
Journal of Computer and System Sciences - Complexity 2001
Derandomizing polynomial identity tests means proving circuit lower bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Derandomizing Arthur-Merlin Games Using Hitting Sets
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
Simple extractors for all min-entropies and a new pseudorandom generator
Journal of the ACM (JACM)
Pseudorandom generators for low degree polynomials
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
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
Uniform derandomization from pathetic lower bounds
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
The pervasive reach of resource-bounded Kolmogorov complexity in computational complexity theory
Journal of Computer and System Sciences
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 that quick hitting set generators can replace quick pseudorandom generators to derandomize any probabilistic two-sided error algorithms. Up to now quick hitting set generators have been known as the general and uniform derandomization method for probabilistic one-sided error algorithms, while quick pseudorandom generators as the generators as the general and uniform method to derandomize probabilistic two-sided error algorithms.Our method is based on a deterministic algorithm that, given a Boolean circuit C and given access to a hitting set generator, constructs a discrepancy set for C. The main novelty is that the discrepancy set depends on C, so the new derandomization method is not uniform (i.e., not oblivious).The algorithm works in time exponential in k(p(n)) where k(*) is the price of the hitting set generator and p(*) is a polynomial function in the size of C. We thus prove that if a logarithmic price quick hitting set generator exists then BPP = P.