How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
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
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Construction of extractors using pseudo-random generators (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Extracting all the randomness and reducing the error in Trevisan's extractors
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
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Weak random sources, hitting sets, and BPP simulations
FOCS '97 Proceedings of the 38th 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
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Extractors and pseudo-random generators with optimal seed length
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Loss-less condensers, unbalanced expanders, and extractors
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Pseudo-random generators for all hardnesses
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The importance of the P versus NP question
Journal of the ACM (JACM)
Derandomizing Arthur-Merlin Games under Uniform Assumptions
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
When Worlds Collide: Derandomization, Lower Bounds, and Kolmogorov Complexity
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
List Decoding: Algorithms and Applications
TCS '00 Proceedings of the International Conference IFIP on Theoretical Computer Science, Exploring New Frontiers of Theoretical Informatics
On the Derandomization of Constant Depth Circuits
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Derandomizing polynomial identity tests means proving circuit lower bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Pseudo-random generators for all hardnesses
Journal of Computer and System Sciences - STOC 2002
Uniform hardness versus randomness tradeoffs for Arthur-Merlin games
Computational Complexity
Simple extractors for all min-entropies and a new pseudorandom generator
Journal of the ACM (JACM)
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
Derandomizing Arthur-Merlin games using hitting sets
Computational Complexity
Extractors from Reed-Muller codes
Journal of Computer and System Sciences - Special issue on FOCS 2001
Low-end uniform hardness vs. randomness tradeoffs for AM
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Pseudorandomness for Approximate Counting and Sampling
Computational Complexity
General Pseudo-random Generators from Weaker Models of Computation
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
The pervasive reach of resource-bounded Kolmogorov complexity in computational complexity theory
Journal of Computer and System Sciences
Reconstructive dispersers and hitting set generators
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
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Various efforts have been made in recent years to derandomize probabilistic algorithms using the complexity theoretic assumption that there exists a problem in E=dtime(2O(n)), that requires circuits of size s(n), (for some function s). These results are based on the NW-generator. For the strong lower bound \math, Impagliazzo and Wigderson get the optimal derandomization: P=BPP. However, for weaker lower bound functions s(n), these constructions fall far short of the natural conjecture for optimal derandomization, namely that bptime(t) \math dtime \math. The gap in these constructions is due to an inherent limitation on efficiency in NW-style pseudo-random generators.In this paper we are able to get derandomization in almost optimal time using any lower bound s(n). We do this by using the NW-generator in a new, more sophisticated way. We view any failure of the generator as a reduction from the given ``hard'' function to its restrictions on smaller input sizes. Thus, either the original construction works (almost) optimally, or one of the restricted functions is (almost) as hard as the original. Any such restriction can then be plugged into the NW-generator recursively. This process generates many ``candidate'' generators, and at least one is guaranteed to be ``good''. Then, to perform the approximation of the acceptance probability of the given circuit, we use ideas from Andreev Clementi and Rolim: we run a tournament between the ``candidate'' generators which yields an accurate estimate.Following Trevisan, we explore information theoretic analogs of our new construction. Trevisan used the NW-generator to construct efficient extractors. However, the inherent limitation of the NW-generator mentioned above makes the extra randomness required by that extractor suboptimal (for certain parameters). Applying our construction, we get an almost optimal disperser.