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Asymmetric unification, or unification with irreducibility constraints, is anewly developed paradigm that arose out of the automated analysis ofcryptographic protocols. However, there are still relatively few asymmetricunification algorithms. In this paper we address this lack by exploring theapplication of automata-based unification methods. We examine the theory of xorwith a homomorphism, ACUNh, from the point of view of asymmetric unification,and develop a new automata-based decision procedure. Then, we adapt a recentlydeveloped asymmetric combination procedure to produce a general asymmetric-ACUNh decision procedure. Finally, we present a new approach for obtaining asolution-generating asymmetric-ACUNh unification automaton. We also compare ourapproach to the most commonly used form of asymmetric unification availabletoday, variant unification.

On Asymmetric Unification for the Theory of XOR with a Homomorphism