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The Confluence Problem for Flat TRSs

  • Ichiro Mitsuhashi
  • Michio Oyamaguch
  • Florent Jacquemard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4120)

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.

Keywords

Term rewriting system Decision problem Confluence Flat 

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References

  1. 1.
    Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)Google Scholar
  2. 2.
    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)Google Scholar
  3. 3.
    Comon, H., Haberstrau, M., Jouannaud, J.-P.: Syntacticness, cycle-syntacticness and shallow theories. Information and Computation 111(1), 154–191 (1994)CrossRefMathSciNetzbMATHGoogle Scholar
  4. 4.
    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)CrossRefMathSciNetzbMATHGoogle Scholar
  5. 5.
    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)Google Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    Jacquemard, F.: Reachability and confluence are undecidable for flat term rewriting systems. Inf. Process. Lett. 87, 265–270 (2003)CrossRefMathSciNetzbMATHGoogle Scholar
  9. 9.
    Jacquemard, F.: Erratum to the paper: Reachability and confluence are undecidable for flat term rewriting system. Research Report LSV-05-09 (2005)Google Scholar
  10. 10.
    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)Google Scholar
  11. 11.
    Mitsuhashi, I., Oyamaguchi, M., Yamada, T.: The reachability and related decision problems for monadic and semi-constructor TRSs. Inf. Process. Lett. (to appear)Google Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    Oyamaguchi, M.: The Church-Rosser property for ground term-rewriting systems is decidable. Theoretical Computer Science 49(1), 43–79 (1987)CrossRefMathSciNetzbMATHGoogle Scholar
  14. 14.
    Oyamaguchi, M.: The reachability and joinability problems for right-ground term-rewriting systems. J. Inf. Process. 13(3), 347–354 (1990)MathSciNetGoogle Scholar
  15. 15.
    Salomaa, K.: Deterministic tree pushdown automata and monadic tree rewriting systems. J. Comput. Syst. Sci. 37, 367–394 (1988)CrossRefMathSciNetzbMATHGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    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)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ichiro Mitsuhashi
    • 1
  • Michio Oyamaguch
    • 1
  • Florent Jacquemard
    • 2
  1. 1.Mie University 
  2. 2.INRIA-Futurs and LSV, UMR CNRS ENS Cachan 

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