Integer circuit evaluation is PSPACE-complete

In this paper, we address the problem of evaluating the integer circuit (IC), or the {U,×,+}-circuit over the set of natural numbers. The problem is a natural extension to the integer expression by L.J. Stockmeyer and A.R. Mayer (1973); and is also studied by P. Mckenzie et al. (1999) in their “Polynomial Replacement System”. We show a polynomial-time algorithm that reduces QBP (quantified Boolean formula) problem to the integer circuit problem. This complements the result of K.W. Wagner (1984) to show that IC problem is PSPACEcomplete. The proof in this paper provides a new perspective to describe PSPACE-completeness