Negation is powerless for Boolean slice functions
SIAM Journal on Computing
The complexity of finite functions
Handbook of theoretical computer science (vol. A)
Journal of Computer and System Sciences
Journal of the ACM (JACM)
On the Fourier spectrum of monotone functions
Journal of the ACM (JACM)
Optimal bounds for the approximation of boolean functions and some applications
Theoretical Computer Science
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Pseudo-random generators for all hardnesses
Journal of Computer and System Sciences - STOC 2002
Hardness amplification within NP
Journal of Computer and System Sciences - Special issue on computational complexity 2002
The Art of Computer Programming, Volume 4, Fascicle 3: Generating All Combinations and Partitions
The Art of Computer Programming, Volume 4, Fascicle 3: Generating All Combinations and Partitions
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
The influence of variables on Boolean functions
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
General Pseudo-random Generators from Weaker Models of Computation
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
KKL, Kruskal-Katona, and Monotone Nets
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Super-polynomial versus half-exponential circuit size in the exponential hierarchy
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Deterministic simulations and hierarchy theorems for randomized algorithms
Deterministic simulations and hierarchy theorems for randomized algorithms
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We investigate whether circuit lower bounds for monotone circuits can be used to derandomize randomized monotone circuits. We show that, in fact, any derandomization of randomized monotone computations would derandomize all randomized computations, whether monotone or not. We prove similar results in the settings of pseudorandom generators and average-case hard functions - that a pseudorandom generator secure against monotone circuits is also secure with somewhat weaker parameters against general circuits, and that an average-case hard function for monotone circuits is also hard with somewhat weaker parameters for general circuits.