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A taxonomy of complexity classes of functions
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Local search for statistical counting
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
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Phase transitions of PP-complete satisfiability problems
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Acceptor-definable counting classes
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STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
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UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
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Theory of Computing Systems
Frobenius's Degree Formula and Toda's Polynomials
Theory of Computing Systems
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Two complexity classes, PP and (+)P, are compared with PH (the polynomial-time hierarchy). The main results are as follows: (1) every set in PH is reducible in a certain sense to a set in PP, an (2) every set in PH is reducible to a set in (+)P under randomized polynomial-time reducibility with two-sided bounded error probability. It follows from these results that neither PP nor (+)P is a subset of or equivalent to PH unless PH collapses to a finite level. This is strong evidence that both classes are strictly harder than PH.