Complexity of Some Problems Concerning Varieties and Quasi-Varieties of Algebras

In this paper we consider the complexity of several problems involving finite algebraic structures. Given finite algebras A and B, these problems ask the following. (1) Do A and B satisfy precisely the same identities? (2) Do they satisfy the same quasi-identities? (3) Do A and B have the same set of term operations? In addition to the general case in which we allow arbitrary (finite) algebras, we consider each of these problems under the restrictions that all operations are unary and that A and B have cardinality two. We briefly discuss the relationship of these problems to algebraic specification theory. Key words. variety, quasi-variety, clone, term-equivalence, computational complexity, logarithmic space, polynomial space, hyperexponential time, nondeterminism AMS subject classifications. Primary, 68Q25; Secondary, 08B15, 08C15, 08A40, 68Q65 PII. S0097539798345944

• Type: Journal
• Year: 2000
• Where: SIAMCOMP
• Authors: Clifford Bergman, Giora Slutzki
• Keywords: Algebraic Structures, Algebras, Problems, SIAMCOMP 2000