Abstract
It is well known that it is undecidable whether a term rewriting system is terminating. We prove in this paper that the property remains undecidable if the system has only one rule.
The preparation of this paper was supported in part by the "GRECO de Programmation" and the PRC "Kathématiques et Informatique".
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
R.V. Book, Thue Systems as Rewriting Systems, in: J.P. Jouannaud, ed., Proceedings of the First International Conference on Rewriting Techniques and Applications, Dijon, France. Springer Lec. Notes Comp. Sci.202 (1985) 63–94. Revised version: J. Symbolic Computation, 3 (1987) 39–68.
N. Dershowitz, Termination, in: J.P. Jouannaud, ed., Proceedings of the First International Conference on Rewriting Techniques and Applications, Dijon, France. Springer Lec. Notes Comp. Sci.202 (1985) 180–224. Revised version: Termination of rewiting. J. Symbolic Computation, 3 (1987) 69–116.
J.V. Guttag, D. Kapur and D.R. Musser, On proving uniform termination and restricted termination of rewriting systems. SIAM J. Comput.12 (1983) 187–214.
G. Huet, D.S. Lankfork, On the uniform halting problem for term rewriting systems, Rapport Laboria 283 (1978), INRIA, Le Chesnay, France.
G. Huet and D.C. Oppen, Equations and rewrite rules: A survey, in: R.V. Book, ed., Formal Language Theory: Perspectives and Open Problems, 1980, pp. 349–405. New York: Academic Press.
J.P. Jouannaud, Editorial of J. Symbolic Computation, 3, 1–2, 1987, 1–2.
R. Lipton and L. Snyder, On the halting of tree replacement systems. Proceedings of the Conference on Theoretical Computer Science, University of Waterloo, Waterloo, Canada, (1977), 43–46.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dauchet, M. (1988). Termination of rewriting is undecidable in the one-rvle case. In: Chytil, M.P., Koubek, V., Janiga, L. (eds) Mathematical Foundations of Computer Science 1988. MFCS 1988. Lecture Notes in Computer Science, vol 324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017149
Download citation
DOI: https://doi.org/10.1007/BFb0017149
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50110-7
Online ISBN: 978-3-540-45926-2
eBook Packages: Springer Book Archive