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).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-31365-3_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31364-6
Online ISBN: 978-3-642-31365-3
eBook Packages: Computer ScienceComputer Science (R0)