Arithmetic Circuits and Polynomial Replacement Systems
نویسندگان
چکیده
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. We contribute a classification of these systems and we investigate their complexity. Diverse problems falling in the scope of this study include, for example, counting proof circuits, and evaluating {∪,+}-circuits over the natural numbers. A number of complexity results are obtained, including a proof that counting proof circuits is #P-complete.
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