Termination of Single-Threaded One-Rule Semi-Thue Systems

  • Wojciech Moczydłowski
  • Alfons Geser
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3467)


This paper is a contribution to the long standing open problem of uniform termination of Semi-Thue Systems that consist of one rule st. McNaughton previously showed that rules incapable of (1) deleting t completely from both sides, (2) deleting t completely from the left, and (3) deleting t completely from the right, have a decidable uniform termination problem. We use a novel approach to show that Premise (2) or, symmetrically, Premise (3), is inessential. Our approach is based on derivations in which every pair of successive steps has an overlap. We call such derivations single-threaded.

Key Words and Phrases:

string rewriting semi-Thue system uniform termination termination one-rule single-rule single-threaded well-behaved 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Book, R., Otto, F.: String-rewriting systems. Texts and Monographs in Computer Science. Springer, New York (1993)zbMATHGoogle Scholar
  2. 2.
    Geser, A.: Is termination decidable for string rewriting with only one rule? Habilitation thesis, Wilhelm-Schickard-Institut, Universität Tübingen, Germany, 201 pages (January 2002)Google Scholar
  3. 3.
    Geser, A., Hofbauer, D., Waldmann, J.: Termination proofs for string rewriting systems via inverse match-bounds. J. Automated Reasoning (2005) (in print)Google Scholar
  4. 4.
    Kobayashi, Y., Katsura, M., Shikishima-Tsuji, K.: Termination and derivational complexity of confluent one-rule string rewriting systems. Theoretical Computer Science 262(1/2), 583–632 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Kurth, W.: Termination und Konfluenz von Semi-Thue-Systemen mit nur einer Regel. Dissertation, Technische Universität Clausthal, Germany (1990)Google Scholar
  6. 6.
    McNaughton, R.: The uniform halting problem for one-rule Semi-Thue Systems. Technical Report 94-18, Dept. of Computer Science, Rensselaer Polytechnic Institute, Troy, NY (August 1994); See also, Correction to ‘The Uniform Halting Problem for One-rule Semi-Thue Systems’, unpublished paper (August 1996)Google Scholar
  7. 7.
    McNaughton, R.: Well-behaved derivations in one-rule Semi-Thue Systems. Technical Report 95-15, Dept. of Computer Science, Rensselaer Polytechnic Institute, Troy, NY (November 1995); See also, Correction by the author to ‘Wellbehaved derivations in one-rule Semi-Thue Systems’, unpublished paper (July 1996)Google Scholar
  8. 8.
    McNaughton, R.: Semi-Thue Systems with an Inhibitor. J. Automated Reasoning 26, 409–431 (1997)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Moczydłowski, W.: Jednoregułowe systemy przepisywania słów. Masters thesis, Warsaw University, Poland (2002)Google Scholar
  10. 10.
    Moczydłowski, W., Geser, A.: Termination of single-threaded onerule Semi-Thue systems. Technical Report TR 02-08 (273), Warsaw University, Available electronically (December 2002), at
  11. 11.
    Salomaa, A.: Theory of Automata. Intl. Series of Monographs in Pure and Applied Mathematics, vol. 100. Pergamon Press, Oxford (1969)zbMATHGoogle Scholar
  12. 12.
    Tucker, J.V.: Computing in algebraic systems. In: Drake, F.F., Wainer, S.S. (eds.) Recursion Theory, its Generalisations and Applications. London Mathematical Society Lecture Note Series, vol. 45, pp. 215–235. Cambridge University Press, Cambridge (1980)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Wojciech Moczydłowski
    • 1
  • Alfons Geser
    • 2
  1. 1.Dept. of Computer ScienceCornell UniversityIthacaUSA
  2. 2.National Institute for Aerospace (NIA)HamptonUSA

Personalised recommendations