How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
The complexity of Boolean functions
The complexity of Boolean functions
Pseudo-random generation from one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of 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
Pseudorandom generators without the XOR Lemma (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Higher lower bounds on monotone size
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Hardness amplification within NP
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the Generation of Cryptographically Strong Pseudo-Random Sequences
Proceedings of the 8th Colloquium on Automata, Languages and Programming
Derandomizing polynomial identity tests means proving circuit lower bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th 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
Potential of the approximation method
FOCS '96 Proceedings of the 37th 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
On derandomization and average-case complexity of monotone functions
Theoretical Computer Science
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The construction of pseudo-random generators (PRGs) has been based on strong assumptions like the existence of one-way functions or exponential lower bounds for the circuit complexity of Boolean functions. Given our current lack of satisfactory progress towards proving these assumptions, we study the implications of constructing PRGs for weaker models of computation to the derandomization of general classes like BPP. More specifically, we show how PRGs that fool monotone circuits could lead to derandomization for general complexity classes, and how the Nisan-Wigderson construction could use hardness results for monotone circuits to produce pseudo-random strings.