Skip to main content
SpringerLink
Log in

On confluence versus strong confluence for one-rule trace-rewriting systems

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

Abstract

Examples of one-rule trace-rewriting systems are given that are confluent but not strongly confluent. This contrasts with the situation for one-rule string-rewriting systems as well as with the situation for one-rule commutative string-rewriting systems.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Dershowitz and J. P. Jouannaud, Rewrite systems, in: J. van Leeuwen (ed.),Handbook of Theoretical Computer Science, Vol. B, Eisevier, Amsterdam, 1990, pp. 243–320.

    Google Scholar 

  2. G. Huet, Confluent reductions: abstract properties and applications to term rewriting systems,Journal of the Association for Computing Machinery,27 (1980), 797–821.

    Google Scholar 

  3. J. P. Jouannaud and H. Kirchner, Completion of a set of rules modulo a set of equations,SIAM Journal on Computing,15 (1986), 1155–1194.

    Google Scholar 

  4. D. E. Knuth and P. Bendix, Simple word problems in universal algebras, in: J. Leech (ed.),Computational Problems in Abstract Algebra, Pergamon Press, New York, 1970, pp. 263–297.

    Google Scholar 

  5. W. Kurth, Termination und Konfluenz von Semi-Thue Systemen mit nur einer Regel, Dissertation, Mathematisch-Naturwissenschaftliche Fakultät, Technische Universität, Clausthal, 1990.

    Google Scholar 

  6. A. Mazurkiewicz, Traces, histories and graphs: instances of a process monoid, in: M. Chytil and V. Koubek (eds.),Proceedings, Mathematical Foundations of Computer Science, Lecture Notes in Computer Science, Vol. 176, Springer-Verlag, Berlin, 1984, pp. 115–133.

    Google Scholar 

  7. P. Narendran and F. Otto, Preperfectness is undecidable for Thue systems containing only length-reducing rules and a single commutation rule,Information Processing Letters,29 (1988), 125–130.

    Google Scholar 

  8. F. Otto and C. Wrathall, A note on Thue systems with a single defining relation,Mathematical Systems Theory,18 (1985), 135–143.

    Google Scholar 

  9. C. Wrathall, Confluence of one-rule Thue systems; in: K. U. Schulz (ed.),Word Equations and Related Topics, Lecture Notes in Computer Science, Vol. 572, Springer-Verlag, Berlin, 1992, pp. 237–246.

    Google Scholar 

  10. C. Wrathall and V Diekert, On confluence of one-rule trace-rewriting systems,Mathematical Systems Theory, this issue, pp. 341–361.

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik/Informatik, Universität Kassel, Postfach, D-34109, Kassel, Germany

    F. Otto

Authors
  1. F. Otto
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Otto, F. On confluence versus strong confluence for one-rule trace-rewriting systems. Math. Systems Theory 28, 363–384 (1995). https://doi.org/10.1007/BF01185402

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01185402

Keywords

Search

Navigation