Skip to main content
SpringerLink
Log in
Book cover

Colloquium on Trees in Algebra and Programming

CAAP 1994: Trees in Algebra and Programming — CAAP'94 pp 261–275Cite as

On the modularity of confluence of constructor-sharing term rewriting systems

  • Contributed Papers
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 787))

Abstract

Toyama's Theorem states that confluence is a modular property of disjoint term rewriting systems. This theorem does not generalize to combined systems with shared constructors. Thus the question arises naturally whether there are sufficient conditions which ensure the modularity of confluence in the presence of shared constructors. In particular, Kurihara and Krishna Rao posed the problem whether there arc interesting sufficient conditions independent of termination. This question appeared as Problem 59 in the list of open problems in the theory of rewriting published recently [DJK93]. The present paper gives an affirmative answer to that question. Among other sufficient criteria, it is shown that confluence is preserved under the combination of constructorsharing systems if the systems arc also normalizing. This in conjunction with the fact that normalization is modular for those systems implies the modularity of semi-completeness.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N. Dershowitz and J.P. Jouannaud. Rewrite Systems. In L. van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. B, chapter 6. North-Holland, 1990.

    Google Scholar 

  2. N. Dershowitz, J.P. Jouannaud, and J.W. Klop. More Problems in Rewriting. In Proceedings of the 5th International Conference on Rewriting Techniques and Applications, pages 468–487. Lecture Notes in Computer Science 690, Springer Verlag, 1993.

    Google Scholar 

  3. B. Grämlich. Generalized Sufficient Conditions for Modular Termination of Rewriting. Applicable Algebra in Engineering, Communication and Computing, 1993. To appear.

    Google Scholar 

  4. M. Kurihara and I. Kaji. Modular Term Rewriting Systems and the Termination. Information Processing Letters 34, pages 1–4, 1990.

    Article  MathSciNet  Google Scholar 

  5. J.W. Klop. Term Rewriting Systems. In S. Abramsky, D. Gabbay, and T. Maibaum, editors, Handbook of Logic in Computer Science, Vol. II, pages 1–116. Oxford University Press, 1992.

    Google Scholar 

  6. J.W. Klop, A. Middeldorp, Y. Toyama, and R. Vrijer. A Simplified Proof of Toyama's Theorem. Report CS-R9156, Centre for Mathematics and Computer Science, Amsterdam, 1991. Revised version to appear in Information Processing Letters.

    Google Scholar 

  7. M. Kurihara and A. Ohuchi. Modular Term Rewriting Systems with Shared Constructors. Journal of Information Processing 14(3), IPS of Japan, pages 357–358, 1991.

    MathSciNet  Google Scholar 

  8. M. Kurihara and A. Ohuchi. Modularity of Simple Termination of Term Rewriting Systems with Shared Constructors. Theoretical Computer Science 103, pages 273–282, 1992.

    Article  Google Scholar 

  9. A. Middeldorp. Modular Properties of Term Rewriting Systems. PhD thesis, Vrije Universiteitte Amsterdam, 1990.

    Google Scholar 

  10. A. Middeldorp and Y. Toyama. Completeness of Combinations of Constructor Systems. Journal of Symbolic Computation 15 (3), pages 331–348, 1993.

    Article  Google Scholar 

  11. E. Ohlebusch. On the Modularity of Termination of Term Rewriting Systems. Report Nr. 11, Universität Bielefeld, 1993.

    Google Scholar 

  12. E. Ohlebusch. Termination is not Modular for Confluent Variable-Preserving Term Rewriting Systems. Submitted, 1993.

    Google Scholar 

  13. J.-C. Raoult and J. Vuillemin. Operational and Semantic Equivalence between Recursive Programs. Journal of the ACM 27(4), pages 772–796, 1980.

    Article  Google Scholar 

  14. Y. Toyama, J.W. Klop, and H.P Barendregt. Termination for the Direct Sum of Left-Linear Term Rewriting Systems. In Proceedings of the 3rd International Conference on Rewriting Techniques and Applications, pages 477–491. Lecture Notes in Computer Science 355, Springer Verlag, 1989.

    Google Scholar 

  15. Y. Toyama. Counterexamples to Termination for the Direct Sum of Term Rewriting Systems. Information Processing Letters 25, pages 141–143, 1987.

    Article  Google Scholar 

  16. Y. Toyama. On the Church-Rosser Property for the Direct Sum of Term Rewriting Systems. Journal of the ACM 34(1), pages 128–143, 1987.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universität Bielefeld, 33501, Bielefeld, Germany

    Enno Ohlebusch

Authors
  1. Enno Ohlebusch
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Sophie Tison

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ohlebusch, E. (1994). On the modularity of confluence of constructor-sharing term rewriting systems. In: Tison, S. (eds) Trees in Algebra and Programming — CAAP'94. CAAP 1994. Lecture Notes in Computer Science, vol 787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017487

Download citation

  • DOI: https://doi.org/10.1007/BFb0017487

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57879-6

  • Online ISBN: 978-3-540-48373-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation