Algebraic Structures with Hard Equivalence and Minimization Problems

Abstract

The relationship between the setting in which an algebraic problem is posed and the complexity of solving the problem is considered. The problems studied are equivalence, minimization, and approximate mimmlzatlon problems for formulas revolving variables, parentheses, operators, and (optionally) constants. General suffioent condmons on an algebraic structure Y for these problems to be NP- or coNP-hard are presented. Apphcations are gwen to a number of specific algebraic structures of independent interest including lattices, semirings, regular algebras, finite fields, rings 7/k, and Boolean nngs. Apphcations are also gwen to systems of rewrite rules and to several simple programming languages. © 1984, ACM. All rights reserved.