Journal of Computer and System Sciences
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
Computational Complexity - Special issue on circuit complexity
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Randomness vs time: derandomization under a uniform assumption
Journal of Computer and System Sciences
In search of an easy witness: exponential time vs. probabilistic polynomial time
Journal of Computer and System Sciences - Complexity 2001
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
Super-bits, Demi-bits, and NP/qpoly-natural Proofs
RANDOM '97 Proceedings of the International Workshop on Randomization and Approximation Techniques in Computer Science
Pseudorandom functions in TC0 and cryptographic limitations to proving lower bounds
Computational Complexity
Pseudo-random generators for all hardnesses
Journal of Computer and System Sciences - STOC 2002
Number-theoretic constructions of efficient pseudo-random functions
Journal of the ACM (JACM)
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
SIAM Journal on Computing
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
Super-polynomial versus half-exponential circuit size in the exponential hierarchy
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Improving exhaustive search implies superpolynomial lower bounds
Proceedings of the forty-second ACM symposium on Theory of computing
Hardness Amplification Proofs Require Majority
SIAM Journal on Computing
Journal of Computer and System Sciences
Non-uniform ACC Circuit Lower Bounds
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Nondeterministic Circuit Lower Bounds from Mildly De-randomizing Arthur-Merlin Games
CCC '12 Proceedings of the 2012 IEEE Conference on Computational Complexity (CCC)
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We study connections between Natural Proofs, derandomization, and the problem of proving "weak" circuit lower bounds such as NEXP ⊄ TC0, which are still wide open. Natural Proofs have three properties: they are constructive (an efficient algorithm A is embedded in them), have largeness (A accepts a large fraction of strings), and are useful (A rejects all strings which are truth tables of small circuits). Strong circuit lower bounds that are "naturalizing" would contradict present cryptographic understanding, yet the vast majority of known circuit lower bound proofs are naturalizing. So it is imperative to understand how to pursue un-Natural Proofs. Some heuristic arguments say constructivity should be circumventable. Largeness is inherent in many proof techniques, and it is probably our presently weak techniques that yield constructivity. We prove: Constructivity is unavoidable, even for NEXP lower bounds. Informally, we prove for all "typical" non-uniform circuit classes C, NEXP ⊄ C if and only if there is a polynomial-time algorithm distinguishing some function from all functions computable by C-circuits. Hence NEXP ⊄ C is equivalent to exhibiting a constructive property useful against C. There are no P-natural properties useful against C if and only if randomized exponential time can be "derandomized" using truth tables of circuits from C as random seeds. Therefore the task of proving there are no P-natural properties is inherently a derandomization problem, weaker than but implied by the existence of strong pseudorandom functions. These characterizations are applied to yield several new results. The two main applications are that NEXP ∩ coNEXP does not have nlog n size ACC circuits, and a mild derandomization result for RP.