How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Expanders, randomness, or time versus space
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Journal of Computer and System Sciences
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Explicit OR-dispersers with polylogarithmic degree
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
Pseudorandom generators without the XOR Lemma (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Extractors and pseudo-random generators with optimal seed length
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Easiness Assumptions and Hardness Tests: Trading Time for Zero Error
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Randomness vs. Time: De-Randomization under a Uniform Assumption
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
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We study how the nondeterminism versus determinism problem and the time versus space problem are related to the problem of derandomization. In particular, we show two ways of derandomizing the complexity class AM under uniform assumptions, which was only known previously under non-uniform assumptions [13,14]. First, we prove that either AM = NP or it appears to any nondeterministic polynomial time adversary that NP is contained in deterministic subexponential time infinitely often. This implies that to any nondeterministic polynomial time adversary, the graph non-isomorphism problem appears to have subexponential-size proofs infinitely often, the first nontrivial derandomization of this problem without any assumption. Next, we show that either all BPP = P, AM = NP, and PH ⊆ ⊕P hold, or for any t(n) = 2Ω(n), DTIME(t(n)) ⊆ DSPACE(tƐ(n)) infinitely often for any constant Ɛ 0. Similar tradeoffs also hold for a whole range of parameters. This improves previous results [17,5] and seems to be the first example of an interesting condition that implies three derandomiztion results at once.