# Complexity of Some Problems in Universal Algebra

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## Abstract

In this paper we consider the complexity of several problems involving finite algebraic structures. Given finite universal algebras **A** and **B**, these problems ask: (1) Do **A** and **B** satisfy precisely the same identities? (2) Do they satisfy the same quasi-identities? and (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.

## Keywords

Unary Algebra Universal Algebra Isomorphism Problem Term Operation Operation Symbol
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