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- W1998469407 abstract "This paper addresses the problems of counting proof-trees (as introduced by Venkateswaran and Tompa) and counting proof-circuits, a related but seemingly more natural question. These problems lead to a common generalization of straight-line programs which we call polynomial replacement systems {PRSs}. We contribute a classification of these systems and we investigate their complexity. Diverse problems falling within the scope of this study include, for example, counting proof-circuits and evaluating ${cup,+}$-circuits over the natural numbers. A number of complexity results are obtained, including a proof that counting proof-circuits is $numP$-complete." @default.
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- W1998469407 date "2004-01-01" @default.
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- W1998469407 title "Arithmetic Circuits and Polynomial Replacement Systems" @default.
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- W1998469407 doi "https://doi.org/10.1137/s009753970139207x" @default.
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