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STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Symmetric alternation captures BPP
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Uniform generation of NP - witnesses using an NP -oracle
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FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
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FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
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Pseudo-random generators for all hardnesses
Journal of Computer and System Sciences - STOC 2002
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Hardness amplification proofs require majority
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Typically-correct derandomization
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SIAM Journal on Computing
The hardness of counting full words compatible with partial words
Journal of Computer and System Sciences
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We study computational procedures that use both randomness and nondeterminism. The goal of this paper is to derandomize such procedures under the weakest possible assumptions.Our main technical contribution allows one to "boost" a given hardness assumption: We show that if there is a problem in EXP that cannot be computed by poly-size nondeterministic circuits then there is one which cannot be computed by poly-size circuits that make non-adaptive NP oracle queries. This in particular shows that the various assumptions used over the last few years by several authors to derandomize Arthur-Merlin games (i.e., show AM = NP) are in fact all equivalent.We also define two new primitives that we regard as the natural pseudorandom objects associated with approximate counting and sampling of NP-witnesses. We use the "boosting" theorem and hashing techniques to construct these primitives using an assumption that is no stronger than that used to derandomize AM.We observe that Cai's proof that $$\rm S^{P}_{2} \subseteq ZPP^{NP}$$ and the learning algorithm of Bshouty et al. can be seen as reductions to sampling that are not probabilistic. As a consequence they can be derandomized under an assumption which is weaker than the assumption that was previously known to suffice.