Abstract
We present a new rule-based method for computing complete sets of rigid E-unifiers, improving on Gallier et al. 's method on several points: sharing of sub-terms is improved; substitution application and rewriting are done implicitly; the search for rigid E-unifiers is guided by the structure of the terms, and needs less guessing.
Our method makes extensive use of the congruence closure algorithm, and builds on it a non-deterministic procedure with six rules. We state its soundness, its completeness — with a sharper notion of completeness than Gallier-, its termination, and get a more elementary proof of the NP-completeness of rigid E-unification.
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Goubault, J. (1993). A rule-based algorithm for rigid E-unification. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1993. Lecture Notes in Computer Science, vol 713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022569
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DOI: https://doi.org/10.1007/BFb0022569
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