Idempotent Anti-unification

In this paper we address two problems related to idempotent anti-unification. First, we show that there exists an anti-unification problem with a single idempotent symbol which has an infinite minimal complete set of generalizations. It means that anti-unification with a single idempotent symbol has infinitary or nullary generalization type, similar to anti-unification with two idem- potent symbols, shown earlier by Loı̈c Pottier. Next, we develop an algorithm, which takes an arbitrary idempotent anti-unification problem and computes a representation of its solution set in the form of a regular tree grammar. The algorithm does not depend on the number of idempotent function symbols in the input terms. The language generated by the grammar is the minimal complete set of generalizations of the given anti-unification problem, which implies that idem- potent anti-unification is infinitary. [NOTE: Submitted for review]