Termination of rewriting is undecidable in the one-rvle case
Part of the Lecture Notes in Computer Science book series (LNCS, volume 324)
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.
Unable to display preview. Download preview PDF.
- 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.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- G. Huet, D.S. Lankfork, On the uniform halting problem for term rewriting systems, Rapport Laboria 283 (1978), INRIA, Le Chesnay, France.Google Scholar
- 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.Google Scholar
- J.P. Jouannaud, Editorial of J. Symbolic Computation, 3, 1–2, 1987, 1–2.Google Scholar
- 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.Google Scholar
© Springer-Verlag Berlin Heidelberg 1988