Abstract
We prove that the properties of reachability, joinability and confluence are undecidable for flat TRSs. Here, a TRS is flat if the heights of the left and right-hand sides of each rewrite rule are at most one.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)
Comon, H., Godoy, G., Nieuwenhuis, R.: The confluence of ground term rewrite systems is decidable in polynomial time. In: Proc. 42nd Symp. Foundations of Computer Science (FOCS 2001), Las Vegas, NV, USA (October 2001)
Comon, H., Haberstrau, M., Jouannaud, J.-P.: Syntacticness, cycle-syntacticness and shallow theories. Information and Computation 111(1), 154–191 (1994)
Dauchet, M., Heuillard, T., Lescanne, P., Tison, S.: Decidability of the confluence of finite ground term rewrite systems and of other related term rewrite systems. Information and Computation 88, 187–201 (1990)
Dershowitz, N., Jouannaud, J.-P.: Rewrite systems. In: Handbook of Theoretical Computer Science, vol. B, pp. 243–320. Elsevier Science Publishers B. V., Amsterdam (1990)
Godoy, G., Tiwari, A.: Confluence of shallow right-linear rewrite systems. In: Ong, L. (ed.) CSL 2005. LNCS, vol. 3634, pp. 541–556. Springer, Heidelberg (2005)
Godoy, G., Tiwari, A., Verma, R.: On the confluence of linear shallow term rewrite systems. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 85–96. Springer, Heidelberg (2003)
Jacquemard, F.: Reachability and confluence are undecidable for flat term rewriting systems. Inf. Process. Lett. 87, 265–270 (2003)
Jacquemard, F.: Erratum to the paper: Reachability and confluence are undecidable for flat term rewriting system. Research Report LSV-05-09 (2005)
Mitsuhashi, I., Oyamaguchi, M., Ohta, Y., Yamada, T.: The joinability and related decision problems for semi-constructor TRSs. Trans., IPS Japan 47(5) (to appear, 2006)
Mitsuhashi, I., Oyamaguchi, M., Yamada, T.: The reachability and related decision problems for monadic and semi-constructor TRSs. Inf. Process. Lett. (to appear)
Nagaya, T., Toyama, Y.: Decidability for left-linear growing term rewriting systems. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, pp. 256–270. Springer, Heidelberg (1999)
Oyamaguchi, M.: The Church-Rosser property for ground term-rewriting systems is decidable. Theoretical Computer Science 49(1), 43–79 (1987)
Oyamaguchi, M.: The reachability and joinability problems for right-ground term-rewriting systems. J. Inf. Process. 13(3), 347–354 (1990)
Salomaa, K.: Deterministic tree pushdown automata and monadic tree rewriting systems. J. Comput. Syst. Sci. 37, 367–394 (1988)
Takai, T., Kaji, Y., Seki, H.: Right-linear finite path overlapping term rewriting systems effectively preserve recognizability. In: Bachmair, L. (ed.) RTA 2000. LNCS, vol. 1833, pp. 246–260. Springer, Heidelberg (2000)
Tiwari, A.: Deciding confluence of certain term rewriting systems in polynomial time. In: Proc. IEEE Symposium on Logic in Computer Science, pp. 447–456. IEEE Society, Los Alamitos (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mitsuhashi, I., Oyamaguch, M., Jacquemard, F. (2006). The Confluence Problem for Flat TRSs. In: Calmet, J., Ida, T., Wang, D. (eds) Artificial Intelligence and Symbolic Computation. AISC 2006. Lecture Notes in Computer Science(), vol 4120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11856290_8
Download citation
DOI: https://doi.org/10.1007/11856290_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-39728-1
Online ISBN: 978-3-540-39730-4
eBook Packages: Computer ScienceComputer Science (R0)