The unification problem for confluent right-ground term rewriting systems |
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Authors: | Michio Oyamaguchi Yoshikatsu Ohta |
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Affiliation: | Faculty of Engineering, Mie University, 1515 Kamihama-cho, Tsu-shi, 514-8507, Japan |
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Abstract: | The unification problem for term rewriting systems (TRSs) is the problem of deciding, for a given TRS R and two terms M and N, whether there exists a substitution θ such that Mθ and Nθ are congruent modulo R (i.e., Mθ↔R*Nθ). In this paper, the unification problem for confluent right-ground TRSs is shown to be decidable. To show this, the notion of minimal terms is introduced and a new unification algorithm for obtaining a substitution whose range consists of minimal terms is proposed. Our result extends the decidability of unification for canonical (i.e., terminating and confluent) right-ground TRSs given by Hullot Proceedings of the 5th Conference on Automated Deduction, LNCS, vol. 87, 1980, p. 318] in the sense that the termination condition can be omitted. |
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Keywords: | Unification Confluence Right-ground Term rewriting systems Decidability |
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