How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity class
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
Expanders, randomness, or time versus space
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
Relativized Arthur-Merlin versus Merlin-Arthur games
Information and Computation
Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Statistical zero-knowledge languages can be recognized in two rounds
Journal of Computer and System Sciences
Journal of the ACM (JACM)
Journal of Computer and System Sciences
Designing programs that check their work
Journal of the ACM (JACM)
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
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Explicit OR-dispersers with polylogarithmic degree
Journal of the ACM (JACM)
On the limits of non-approximability of lattice problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
STOC '98 Proceedings of the thirtieth 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
Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Extracting randomness: a survey and new constructions
Journal of Computer and System Sciences
Extractors and pseudo-random generators with optimal seed length
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Loss-less condensers, unbalanced expanders, and extractors
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Pseudo-random generators for all hardnesses
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
In search of an easy witness: exponential time vs. probabilistic polynomial time
Journal of Computer and System Sciences - Complexity 2001
On Resource-Bounded Measure and Pseudorandomness
Proceedings of the 17th Conference on Foundations of Software Technology and Theoretical Computer Science
Extracting Randomness: How and Why - A survey
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Easiness Assumptions and Hardness Tests: Trading Time for Zero Error
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
A Complete Promise Problem for Statistical Zero-Knowledge
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Randomness vs. Time: De-Randomization under a Uniform Assumption
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Derandomizing Arthur-Merlin Games Using Hitting Sets
FOCS '99 Proceedings of the 40th 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
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Pseudorandomness and Average-Case Complexity via Uniform Reductions
CCC '02 Proceedings of the 17th IEEE Annual Conference on Computational Complexity
Simple Extractors for All Min-Entropies and a New Pseudo-Random Generator
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Low-end uniform hardness vs. randomness tradeoffs for AM
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
If NP Languages are Hard on the Worst-Case, Then it is Easy to Find Their Hard Instances
Computational Complexity
Pseudorandomness and Average-Case Complexity Via Uniform Reductions
Computational Complexity
A (de)constructive approach to program checking
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Pseudorandom Generators and Typically-Correct Derandomization
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Typically-correct derandomization
ACM SIGACT News
Relations between average-case and worst-case complexity
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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Impagliazzo and Wigderson proved a uniform hardness vs. randomness "gap theorem" for BPP. We show an analogous result for AM: Either Arthur-Merlin protocols are very strong and everything in E = DTIME(2O(n)) can be proved to a subexponential time verifier, or else Arthur-Merlin protocols are weak and every language in AM has a polynomial time nondeterministic algorithm such that it is infeasible to come up with inputs on which the algorithm fails. We also show that if Arthur-Merlin protocols are not very strong (in the sense explained above) then AM ∩ coAM = NP ∩ coNP.Our technique combines the nonuniform hardness versus randomness tradeoff of Miltersen and Vinodchandran with "instance checking". A key ingredient in our proof is identifying a novel "resilience" property of hardness vs. randomness tradeoffs.