Abstract
Unification modulo the theory defined by a single equation which specifies that a binary operator distributes synchronously over another binary operator is shown to be undecidable. It is the simplest known theory, to our knowledge, for which unification is undecidable: it has only one defining axiom and moreover, every congruence class is finite (so the matching problem is decidable).
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References
Anantharaman, S., Erbatur, S., Lynch, C., Narendran, P., Rusinowitch, M.: Unification modulo Synchronous Distributivity. Technical Report SUNYA-CS-12-01, Dept. of Computer Science, University at Albany—SUNY (2012), http://www.cs.albany.edu/~ncstrl/treports/Data/README.html
Baader, F., Snyder, W.: Unification Theory. In: Handbook of Automated Reasoning, pp. 440–526. Elsevier Sc. Publishers B.V. (2001)
Baader, F., Nipkow, T.: Rewriting and all that. Cambridge University Press, New York (1998)
Chaum, D.: Security without Identification: Transaction System to Make Big Brother Obsolete. Communications of the ACM 28(2), 1030–1044 (1985)
Hoare, C.A.R., Hussain, A., Möller, B., O’Hearn, P.W., Petersen, R.L., Struth, G.: On Locality and the Exchange Law for Concurrent Processes. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 250–264. Springer, Heidelberg (2011)
Hooper, P.K.: The Undecidability of the Turing Machine Immortality Problem. J. Symbolic Logic 31(2), 219–234 (1966)
Jahama, S., Kfoury, A.J.: A General Theory of Semi-Unification. Technical Report 1993-018, Dept. of Computer Science, Boston University (December 1993)
Jouannaud, J.-P., Kirchner, C.: Solving equations in abstract algebras: a rule-based survey of unification. In: Computational Logic: Essays in Honor of Alan Robinson, pp. 360–394. MIT Press, Boston (1991)
Kapur, D., Narendran, P.: The Knuth-Bendix Completion Procedure and Thue Systems. SIAM Journal on Computing 14(4), 1052–1072 (1985)
Kfoury, A.J., Tiuryn, J., Urzyczyn, P.: The Undecidability of the Semi-Unification Problem. Information and Computation 102(1), 83–101 (1993)
Schmidt-Schauß, M.: A Decision Algorithm for Distributive Unification. Theoretical Comp. Science 208(1-2), 111–148 (1998)
Snyder, W.: A Proof Theory for General Unification, pp. 25–26. Birkhäuser, Basel (1991)
Tiden, E., Arnborg, S.: Unification Problems with One-sided Distributivity. Journal of Symbolic Computation 3(1–2), 183–202 (1987)
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Anantharaman, S., Erbatur, S., Lynch, C., Narendran, P., Rusinowitch, M. (2012). Unification Modulo Synchronous Distributivity. In: Gramlich, B., Miller, D., Sattler, U. (eds) Automated Reasoning. IJCAR 2012. Lecture Notes in Computer Science(), vol 7364. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31365-3_4
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DOI: https://doi.org/10.1007/978-3-642-31365-3_4
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