The Complexity of Iterated Multiplication

Abstract

For a monoid G, the iterated multiplication problem is the computation of the product of n elements from G. By refining known completeness arguments, we show that as G varies over a natural series of important groups and monoids, the iterated multiplication problems are complete for most natural, low-level complexity classes. The completeness is with respect to "first-order projections"-low-level reductions that do not obscure the algebraic nature of these problems. © 1995 Academic Press. All rights reserved.