AC-complete Unification and its Application to Theorem Proving (1996)
| Venue: | IN PROCEEDINGS OF THE 7TH INTERNATIONAL CONFERENCE ON REWRITING TECHNIQUES AND APPLICATIONS |
| Citations: | 5 - 0 self |
BibTeX
@INPROCEEDINGS{Boudet96ac-completeunification,
author = {Alexandre Boudet and Evelyne Contejean and Claude Marché},
title = {AC-complete Unification and its Application to Theorem Proving},
booktitle = {IN PROCEEDINGS OF THE 7TH INTERNATIONAL CONFERENCE ON REWRITING TECHNIQUES AND APPLICATIONS},
year = {1996},
pages = {18--32},
publisher = {Springer-Verlag}
}
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Abstract
The inefficiency of AC-completion is mainly due to the doubly exponential number of AC-unifiers and thereby of critical pairs generated. We present AC-complete E-unification, a new technique whose goal is to reduce the number of AC-critical pairs inferred by performing unification in a extension E of AC (e.g. ACU, Abelian groups, Boolean rings, ...) in the process of normalized completion [21]. The idea is to represent complete sets of AC-unifiers by (smaller) sets of E-unifiers. Not only the theories E used for unification have exponentially fewer most general unifiers than AC, but one can remove from a complete set of E-unifiers those solutions which have no E-instance which is an AC-unifier. First, we define AC-complete E-unification and describe its fundamental properties. We show how AC-complete E-unification can be done in the elementary case, and how the known combination techniques for unification algorithms can be reused for our purposes. Finally, we give some evidence of t...
