Arithmetic Circuits and Polynomial Replacement Systems

Authors:
Pierre McKenzie;Heribert Vollmer;Klaus W. Wagner
Affiliations:
-;-;-
Venue:
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
Year:
2000

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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. 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. The former is shown #P-complete, the latter to be equivalent to a particular problem for replacement systems.