Computational limitations of small-depth circuits
Computational limitations of small-depth circuits
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
On read-once vs. multiple access to randomness in logspace
Theoretical Computer Science - Special issue on structure in complexity theory
Random-self-reducibility of complete sets
SIAM Journal on Computing
Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs
Journal of Computer and System Sciences
Journal of Computer and System Sciences
Extractors and pseudorandom generators
Journal of the ACM (JACM)
Randomness vs time: derandomization under a uniform assumption
Journal of Computer and System Sciences
Graph Nonisomorphism Has Subexponential Size Proofs Unless the Polynomial-Time Hierarchy Collapses
SIAM Journal on Computing
In search of an easy witness: exponential time vs. probabilistic polynomial time
Journal of Computer and System Sciences - Complexity 2001
Derandomization That Is Rarely Wrong from Short Advice That Is Typically Good
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Uniform hardness versus randomness tradeoffs for Arthur-Merlin games
Computational Complexity
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Low-end uniform hardness vs. randomness tradeoffs for AM
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Pseudorandom Bits for Constant-Depth Circuits with Few Arbitrary Symmetric Gates
SIAM Journal on Computing
Pseudorandomness and Average-Case Complexity Via Uniform Reductions
Computational Complexity
Undirected connectivity in log-space
Journal of the ACM (JACM)
Exposure-Resilient Extractors and the Derandomization of Probabilistic Sublinear Time
Computational Complexity
Weak Derandomization of Weak Algorithms: Explicit Versions of Yao's Lemma
CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
An introduction to randomness extractors
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
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The area of derandomization attempts to provide efficient deterministic simulations of randomized algorithms in various algorithmic settings. Goldreich and Wigderson introduced a notion of "typically-correct" deterministic simulations, which are allowed to err on few inputs. In this paper we further the study of typically-correct derandomization in two ways. First, we develop a generic approach for constructing typically-correct derandomizations based on seed-extending pseudorandom generators, which are pseudorandom generators that reveal their seed. We use our approach to obtain both conditional and unconditional typically-correct derandomization results in various algorithmic settings. We show that our technique strictly generalizes an earlier approach by Shaltiel based on randomness extractors, and simplifies the proofs of some known results. We also demonstrate that our approach is applicable in algorithmic settings where earlier work did not apply. For example, we present a typically-correct polynomial-time simulation for every language in BPP based on a hardness assumption that is weaker than the ones used in earlier work. Second, we investigate whether typically-correct derandomization of BPP implies circuit lower bounds. Extending the work of Kabanets and Impagliazzo for the zero-error case, we establish a positive answer for error rates in the range considered by Goldreich and Wigderson. In doing so, we provide a simpler proof of the zero-error result. Our proof scales better than the original one and does not rely on the result by Impagliazzo, Kabanets, and Wigderson that NEXP having polynomial-size circuits implies that NEXP coincides with EXP.