Abstract
The class of equational theories defined by so-called unify-stable presentations was recently introduced, as well as a complete and terminating unification algorithm modulo any such theory. However, two equivalent presentations may have a different status, one being unify-stable and the other not. The problem of deciding whether an equational theory admits a unify-stable presentation or not thus remained open. We show that this problem is decidable and that we can compute a unify-stable presentation for any theory, provided one exists. We also provide a fairly efficient algorithm for such a task, and conclude by proving that deciding whether a theory admits a unify-stable presentation and computing such a presentation are problems in the Luks equivalence class.
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.
References
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)
Boy de la Tour, T., Echenim, M.: Determining unify-stable presentations (long version), http://www-leibniz.imag.fr/~boydelat/papers/
Boy de la Tour, T., Echenim, M.: Overlapping leaf permutative equations. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 430–444. Springer, Heidelberg (2004)
Boy de la Tour, T., Echenim, M.: Permutative rewriting and unification. Information and Computation 25(4), 624–650 (2007)
Butler, G. (ed.): Fundamental Algorithms for Permutation Groups. LNCS, vol. 559. Springer, Heidelberg (1991)
The GAP Group. GAP – Groups, Algorithms, and Programming, Version 4.4 (2006), http://www.gap-system.org
Hoffmann, C. (ed.): Group-Theoretic Algorithms and Graph Isomorphism. LNCS, vol. 136. Springer, Heidelberg (1982)
Kapur, D., Narendran, P.: Double-exponential complexity of computing a complete set of ac-unifiers. In: Scedrov, A. (ed.) LICS 1992, pp. 11–21. IEEE Computer Society Press, Washington, DC, USA (1992)
Kirchner, C., Klay, F.: Syntactic theories and unification. In: Mitchell, J. (ed.) LICS 1990, pp. 270–277. IEEE Computer Society Press, Washington, DC, USA (1990)
Lankford, D.S., Ballantyne, A.: Decision procedures for simple equational theories with permutative axioms: complete sets of permutative reductions. Technical report, Univ. of Texas at Austin, Dept. of Mathematics and Computer Science (1977)
Narendran, P., Otto, F.: Single versus simultaneous equational unification and equational unification for variable-permuting theories. J. Autom. Reasoning 19(1), 87–115 (1997)
Nieuwenhuis, R.: Decidability and complexity analysis by basic paramodulation. Information and Computation 147(1), 1–21 (1998)
Schmidt-Schauß, M.: Solution to problems p140 and p141. Bulletin of the EATCS 34, 274–275 (1988)
Schmidt-Schauß, M.: Unification in permutative equational theories is undecidable. J. Symb. Comput. 8(4), 415–421 (1989)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Boy de la Tour, T., Echenim, M. (2007). Determining Unify-Stable Presentations. In: Baader, F. (eds) Term Rewriting and Applications. RTA 2007. Lecture Notes in Computer Science, vol 4533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73449-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-73449-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73447-5
Online ISBN: 978-3-540-73449-9
eBook Packages: Computer ScienceComputer Science (R0)