CIRCUITS, MATRICES, AND NONASSOCIATIVE COMPUTATION

We consider the complexity of various computational problems over nona ssociative algebraic structures. Specifically, we look at the problem of evaluating circuits, formulas, and words, over both nonassociative structures themselves and over matrices with elements in these structu res. Extending past work, we show that such problems can characterize a wide variety of complexity classes up to and including NP. As an exa mple, the word (i.e., iterated multiplication) problems involving a se quence of O(log(k) n) matrices over a structure ( S; +,) in which (S; +) is a monoid or an aperiodic monoid are complete for NCk+1 and for A C(k), respectively, and a word problem variant involving matrices of s ize O(log(k) n) is complete for SCk. (C) 1995 Academic Press. Inc.