Pseudo-random generators for all hardnesses
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the complexity of approximating the VC dimension
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
Extractors: optimal up to constant factors
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
Batch codes and their applications
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Better extractors for better codes?
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Uniform hardness versus randomness tradeoffs for Arthur-Merlin games
Computational Complexity
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
Deterministic Extractors for Affine Sources over Large Fields
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Can every randomized algorithm be derandomized?
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On the randomness complexity of efficient sampling
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Lower bounds for non-black-box zero knowledge
Journal of Computer and System Sciences - Special issue on FOCS 2003
Language compression and pseudorandom generators
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
Infeasibility of instance compression and succinct PCPs for NP
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Simple extractors via constructions of cryptographic pseudo-random generators
Theoretical Computer Science
On the hardness against constant-depth linear-size circuits
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Infeasibility of instance compression and succinct PCPs for NP
Journal of Computer and System Sciences
Deterministic extractors for independent-symbol sources
IEEE Transactions on Information Theory
Extracting Kolmogorov complexity with applications to dimension zero-one laws
Information and Computation
Another motivation for reducing the randomness complexity of algorithms
Studies in complexity and cryptography
Simple extractors via constructions of cryptographic pseudo-random generators
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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
Computational complexity since 1980
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Deterministic extractors for independent-symbol sources
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Extracting kolmogorov complexity with applications to dimension zero-one laws
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Relations between average-case and worst-case complexity
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Impossibility results on weakly black-box hardness amplification
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
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We present a simple, self-contained extractor construction that produces good extractors for all min-entropies (min-entropy measures the amount of randomness contained in a weak random source). Our construction is algebraic and builds on a new polynomial-based approach introduced by Ta-Shma, Zuckerman, and Safra [37]. Using our improvements, we obtain, for example, an extractor with output length m = k1 - \delta and seed length O(log n). This matches the parameters of Trevisan's breakthrough result [38] and additionally achieves those parameters for small min-entropies k. Extending [38] to small k has been the focus of a sequence of recent works [15, 26, 35]. Our construction gives a much simpler and more direct solution to this problem.Applying similar ideas to the problem of building pseudorandom generators, we obtain a new pseudo-random generator construction that is not based on the NW generator [21], and turns worst-case hardness directly into pseudorandomness. The parameters of this generator match those in [16, 33] and in particular are strong enough to obtain a new proof that P = BPP if E requires exponential size circuits.Essentially the same construction yields a hitting set generator with optimal seed length that outputs s^{\Omega (1)} bits when given a function that requires circuits of size s (for any s). This implies a hardness versus randomness tradeoff for RP and BPP that is optimal (up to polynomial factors), solving an open problem raised by [14]. Our generators can also be used to derandomize AM in a way that improves and extends the results of [4, 18, 20].