Skip to main content
SpringerLink
Log in

Chain properties of rule closures

  • Contributed Papers
  • Conference paper
  • First Online:
STACS 89 (STACS 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 349))

Included in the following conference series:

Abstract

This article presents an introduction to the generalization of the crossed rule approach to the detection of Knuth-Bendix completion procedure divergence. It introduces the closure chains, which are special rule closures constructed by means of particular substitution operations and operators, as a suitable formalism for a progress in this direction. Supporting substitution algebra is developed first, followed by considerations concerning rule closures in general, and concluded by investigation of closure chain properties.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3(1 & 2):69–116, 1987. Special issue on Rewriting Techniques and Applications.

    Google Scholar 

  2. J.V. Guttag, D. Kapur, and D.R. Musser. On proving uniform termination and restricted termination of rewrite systems. SIAM Journal on Computation, 12(1):189–214, February 1983.

    Google Scholar 

  3. M. Hermann. Crossed term rewriting systems. Research report, Centre de Recherche en Informatique de Nancy, 1988. In preparation.

    Google Scholar 

  4. M. Hermann and I. Prívara. On nontermination of Knuth-Bendix algorithm. In L. Kott, editor, Proceedings of the 13th ICALP Conference, Rennes (France), pages 146–156, Springer Verlag, 1986. Lecture Notes in Computer Science, volume 226.

    Google Scholar 

  5. G. Huet. A complete proof of correctness of the Knuth-Bendix completion algorithm. Journal of Computer and System Science, 23(1):11–21, August 1981. Also as: Rapport 25, INRIA, 1980.

    Google Scholar 

  6. D.S. Lankford and D.R. Musser. A Finite Termination Criterion. Unpublished draft, Information Sciences Institute, University of Southern California, Marina-del-Rey, CA, 1978.

    Google Scholar 

  7. P. Narendran and J. Stillman. It is undecidable whether the Knuth-Bendix completion procedure generates a crossed pair. In Proceedings of the 6th STACS, Paderborn (FRG), Springer Verlag, February 1989. Lecture Notes in Computer Science.

    Google Scholar 

  8. B. K. Rosen. Tree-manipulating systems and Church-Rosser theorems. Journal of ACM, 20(1):160–187, January 1973.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre de Recherche en Informatique de Nancy CNRS and INRIA-Lorraine Campus Scientifique, BP 239, 54506, Vandœuvre-les-Nancy, France

    Miki Hermann

Authors
  1. Miki Hermann
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

B. Monien R. Cori

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hermann, M. (1989). Chain properties of rule closures. In: Monien, B., Cori, R. (eds) STACS 89. STACS 1989. Lecture Notes in Computer Science, vol 349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028997

Download citation

  • DOI: https://doi.org/10.1007/BFb0028997

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50840-3

  • Online ISBN: 978-3-540-46098-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation