Complexity of some problems concerning varieties and quasi-varieties of algebras

In this paper we consider the complexity of several problems involving fini te 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 o f term operations? In addition to the general case in which we allow arbitrary (finite) algebr as, we consider each of these problems under the restrictions that all oper ations are unary and that A and B have cardinality two. We briefly discuss the relationship of these problems to algebraic specification theory.