Asymmetric Unification and the Combination Problem in Disjoint Theories

Asymmetric unification is a new paradigm for unification modulo theories that introduces irreducibility constraints on one side of a unification problem. It has important applications in symbolic cryptographic protocol analysis, for which it is often necessary to put irreducibility constraints on portions of a state. However many facets of asymmetric unification that are of particular interest, including its behavior under combinations of disjoint theories, remain poorly understood. In this paper we give a new formulation of the method for unification in the combination of disjoint equational theories developed by Baader and Schulz that both gives additional insights into the disjoint combination problem in general, and furthermore allows us to extend the method to asymmetric unification, thus giving the first unification method for asymmetric unification in the combination of disjoint theories