Determining unify-stable presentations

Authors:
Thierry Boy de la Tour;Mnacho Echenim
Affiliations:
CNRS, Laboratoire d'Informatique de Grenoble, France;Dipartimento di Informatica, Università degli Studi di Verona, Italy
Venue:
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Year:
2007

Citing 5
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Abstract

The class of equational theories defined by so-called unify-stable presentations was recently introduced, as well as a complete and terminating unification algorithm modulo any such theory. However, two equivalent presentations may have a different status, one being unify-stable and the other not. The problem of deciding whether an equational theory admits a unify-stable presentation or not thus remained open. We show that this problem is decidable and that we can compute a unify-stable presentation for any theory, provided one exists. We also provide a fairly efficient algorithm for such a task, and conclude by proving that deciding whether a theory admits a unify-stable presentation and computing such a presentation are problems in the Luks equivalence class.