Abstract
We present a finite, special, and confluent string-rewriting system for which the word matching problem is undecidable. Since the word matching problem is the non-symmetric restriction of the word unification problem, this presents a non-trivial improvement of the recent result that for this type of string-rewriting systems, the word unification problem is undecidable (Otto 1995). In fact, we show that our undecidability result remains valid even when we only consider very restricted instances of the word matching problem.
Partially supported by the NSF grants CCR-9404930 and INT-9401087.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
F. Baader and J.S. Siekmann. Unification theory. In: D.M. Gabbay, C.J. Hogger, and J.A. Robinson (eds.), Handbook of Logic in Artificial Intelligence and Logic Programming, Oxford University Press, 1994.
R. Book and F. Otto. String-Rewriting Systems. Springer Verlag, New York, 1993.
Y. Cochet. Church-Rosser congruences on free semigroups. Colloquia Mathematica Societatis János Bolyai 20 (1976) 51–60.
N. Dershowitz and J.P. Jouannaud. Rewrite systems. In: J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, Vol. B: Formal Models and Semantics, Elsevier, Amsterdam, 1990, pages 243–320.
J. Jaffar. Minimal and complete word unification. Journal Association Computing Machinery 37 (1990) 47–85.
J.P. Jouannaud and C. Kirchner. Solving equations in abstract algebras: a rule-based survey of unification. In: J.L. Lassez and G. Plotkin (eds.), Computational Logic: Essays in Honor of Alan Robinson, MIT Press, 1991, pages 360–394.
A. Kościelski and L. Pacholski. Makanin's group algorithm is not primitive recursive. Theoretical Computer Science, to appear.
G.S. Makanin. The problem of solvability of equations in a free semigroup. Mat. Sbornik 103 (1977) 147–236.
G.S. Makanin. Equations in a free group. Math. USSR Izvestija 21 (1983) 483–546.
G.S. Makanin. Decidability of the universal and positive theories of a free group. Math. USSR Izvestija 25 (1985) 75–88.
G.S. Makanin and H. Abdulrab. On general solution of word equations. In: J. Karhumäki, H. Maurer, and G. Rozenberg (eds.), Results and Trends in Theoretical Computer Science, Lecture Notes Computer Science 812, Springer Verlag, Berlin, 1994, pages 251–263.
P. Narendran and F. Otto. Some results on equational unification. In: M.E. Stickel (ed.), Proceedings 10th CADE, Lecture Notes in Artificial Intelligence 449, Springer Verlag, Berlin, 1990, pages 276–291.
F. Otto. Solvability of word equations modulo finite special and confluent string-rewriting systems is undecidable in general. Information Processing Letters 53 (1995) 237–242.
J.P. Pecuchet. Equations avec Constantes et Algorithme de Makanin. These 3e Cycle, Université de Rouen, France, Dec. 1981.
K.U. Schulz. Makanin's algorithm for word equations-Two improvements and a generalization. In: K.U. Schulz (ed.), Word Equations and Related Topics, Proceedings, Lecture Notes Computer Science 572, Springer Verlag, Berlin, 1990, pages 85–150.
K.U. Schulz. Word unification and transformation of generalized equations. Journal of Automated Reasoning 11 (1993) 149–184.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Narendran, P., Otto, F. (1997). The word matching problem is undecidable for finite special string-rewriting systems that are confluent. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_218
Download citation
DOI: https://doi.org/10.1007/3-540-63165-8_218
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63165-1
Online ISBN: 978-3-540-69194-5
eBook Packages: Springer Book Archive