The Complexity of Membership Problems for Circuits over Sets of Natural Numbers
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In this paper, we address the problem of evaluating the Integer Circuit (IC), or the {cup, times, +}-circuit over the set of natural numbers. The problem is a natural extension to the integer expression by Stockmeyer and Mayer, and is studied by Mckenzie, Vollmer and Wagner in their 驴Polynomial Replacement System驴. We show a polynomial-time algorithm that reduces QBF (Quantified Boolean Formula) problem to the Integer Circuit problem. This complements the result of Wagner to show that IC problem is PSPACE-complete. The proof in this paper provides a new perspective to describe PSPACE-completeness.