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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References
P. Andrews. Theorem proving via general matings. J. ACM, 28(2):193–214, April 1981.
L. Bachmair, N. Dershowitz, and D. Plaisted. Completion without failure. In Resolution of Equations in Algebraic Structures, volume 2, pages 1–30. Academic Press, 1989.
B. Beckert. A completion-based method for adding equality to free variable semantic tableaux. In Workshop on Theorem Proving with Analytic. Tableaux and Related Methods, number MPI-I-93-213, pages 19–22, Marseille, France, avril 1993.
W. Bibel. Tautology testing with a generalized matrix reduction method. Theoretical Computer Science, 8:31–44, 1979.
W. Bibel. Automated Theorem Proving. Vieweg, 2nd, revised edition, 1987.
P. K. Downey, R. Sethi, and R. E. Tarjan. Variations on the common subexpression problem. J. ACM, 27(4):758–771, 1980.
J. Gallier. Logic for Computer Science — Foundations of Automatic Theorem Proving. John Wiley and Sons, 1987.
J. Gallier, P. Narendran, S. Raatz, and W. Snyder. Theorem proving using equational matings and rigid E-unification. J. ACM, 39(2):377–429, April 1992.
J. Gallier, S. Raatz, and W. Snyder. Theorem proving using rigid E-unification equational matings. In LICS, pages 338–346. IEEE, 1987.
J. Gallier, W. Snyder, P. Narendran, and D. Plaisted. Rigid E-unification is NP-complete. In LICS, pages 218–227. IEEE, 1988.
J. Goubault. Démonstration automatique en logique classique: complexité et méthodes. PhD thesis, Laboratoire d'informatique de l'école polytechnique, 1993.
J. Goubault. A rule-based algorithm for rigid E-unification. Technical Report 93024, Bull S.A., juin 1993.
J.-P. Jouannaud and C. Kirchner. Solving equations in abstract algebras: a rule-based survey of unification. Technical report, LRI, CNRS UA 410, March 1990.
K. Mehlhorn and A. Tsakalidis. Data structures. In J. v. Leeuwen, editor, Handbook of Theoretical Computer Science, chapter 6, pages 301–341. Elsevier, 1990.
G. Nelson and D. G. Oppen. Fast decision procedures based on congruence closure. J. ACM, 27(2):356–364, April 1980.
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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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