Fragments of the universal theory of algebraic structures — polynomial reductions

Abstract

The purpose of this note is to establish some reductions, operating in polynomial time, between fragments of the universal theory of a given class K of similar algebras, thus arriving at complexity upper bounds of one fragment in terms of complexity of another fragment. Even if our primary interest is in varieties K of residuated lattices, we formulate the problem in general terms to assess the limitations of this method. Parts of the material are generalizations of results already appearing in literature.