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STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
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On the complexity of the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Retraction of probabilistic computation and linear time
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Journal of the ACM (JACM)
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Journal of the ACM (JACM)
A Probabilistic-Time Hierarchy Theorem for "Slightly Non-uniform" Algorithms
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
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FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
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Foundations and Trends® in Theoretical Computer Science
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CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
From logarithmic advice to single-bit advice
Studies in complexity and cryptography
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TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Time hierarchies for sampling distributions
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We show that for any reasonable semantic model of computation and for any positive integer a and rationals 1 驴 c d, there exists a language computable in time n d with a bits of advice but not in time n c with a bits of advice. Our result implies the first such hierarchy theorem for randomized machines with zero-sided error, quantum machines with one- or zero-sided error, unambiguous machines, symmetric alternation, Arthur.Merlin games of any signature, etc. Our argument yields considerably simpler proofs of known hierarchy theorems with one bit of advice for randomized and quantum machines with two-sided error.Our paradigm also allows us to derive stronger separation results in which the machine with the smaller running time can receive more advice than the one with the larger running time. We present a unified way to derive such results for randomized and quantum machines with two-sided error and for randomized machines with one-sided error.