Restrictions of congruences generated by finite canonical string-rewriting systems

  • Friedrich Otto
Regular Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 355)


Let Σ1 be a subalphabet of Σ2. and let R1 and R2 be finite string-rewriting systems on Σ1 and Σ2, respectively. If the congruence \(\overset * \longleftrightarrow\)R1 and the congruence \(\overset * \longleftrightarrow\)R2 generated by R2 coincide on Σ1*, then R1 can be seen as representing the restriction of the system R2 to the subalphabet Σ1. Is this property decidable ? This question is investigated for several classes of finite canonical string-rewriting systems.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    J. Avenhaus, K. Madlener, Subrekursive Komplexität bei Gruppen II. Der Einbettungssatz von Higman für entscheidbare Gruppen. Acta Informatica 9 (1978), 183–193.Google Scholar
  2. 2.
    G. Bauer, Zur Darstellung von Monoiden durch Regelsysteme, Ph.D. Dissertation, Fachbereich Informatik. Universität Kaiserslautern, 1981.Google Scholar
  3. 3.
    G. Bauer, F. Otto, Finite complete rewriting systems and the complexity of the word problem. Acta Inf. 21 (1984), 521–540.Google Scholar
  4. 4.
    J. A. Bergstra, J.V. Tucker, A characterization of computable data types by means of a finite, equational specification method; Technical Report, Mathematical Centrum, Amsterdam, Holland, 1979. Preprint IW 124/79, 1979.Google Scholar
  5. 5.
    L. Boasson, Grammaires a non-terminaire separes, 7th ICALP. Lecture Notes in Computer Science 85 (1980), 105–118.Google Scholar
  6. 6.
    R.V. Book, Thue systems as rewriting systems. J. Symbolic Computation 3 (1987). 39–68.Google Scholar
  7. 7.
    R.V. Book, C. O'Dunlaing, Thue congruences and the Church-Rosser property, Semigroup Forum 22 (1981), 325–331.Google Scholar
  8. 8.
    C. Frougny: Une famille de langages algebriques congruentiels; les languages a non-terminaire separes; These de 3eme cycle de l'universite de Paris VII, 1980.Google Scholar
  9. 9.
    M. Jantzen: A note on a special one-rule semi-Thue system, Inf. Proc. Letters 21 (1985), 135–140.Google Scholar
  10. 10.
    D. Kapur, P. Narendran: A finite Thue system with decidable word problem and without equivalent finite canonical system; Theoretical Computer Science 35 (1985), 337–344.Google Scholar
  11. 11.
    D. Kapur, P. Narendran: The Knuth-Bendix completion procedure and Thue systems; SIAM J. on Computing 14 (1985), 1052–1072.Google Scholar
  12. 12.
    D. Knuth, P. Bendix: Simple word problems in universal algebras; in: J. Leech (ed.), Computational Problems in Abstract Algebra, Oxford: Pergamon Press, 1970, pp. 263–297.Google Scholar
  13. 13.
    A.A. Markov: Impossibility of algorithms for recognizing some properties of associative systems; Dokl. Akad. Nauk SSSR 77 (1951), 953–956.Google Scholar
  14. 14.
    A. Mostowski: Review of [13]; J. of Symbolic Logic 17 (1952), 151–152.Google Scholar
  15. 15.
    P. Narendran, C. O'Dunlaing: Cancellativity in finitely presented semigroups; Journal of Symbolic Computation, to appear.Google Scholar
  16. 16.
    P. Narendran, F. Otto: Some polynomial-time algorithms for finite monadic Church-Rosser Thue systems, Technical Report (87-20), Department of Computer Science, State University of New York, Albany, 1987, also: Theoretical Computer Science, to appear.Google Scholar
  17. 17.
    C. O'Dunlaing: Undecidable questions of Thue systems; Theoretical Computer Science 23 (1983), 339–345.Google Scholar
  18. 18.
    F. Otto: Some undecidability results for non-monadic Church-Rosser Thue systems; Theoretical Computer Science 33 (1984), 261–278.Google Scholar
  19. 19.
    F. Otto: On two problems related to cancellativity, Sernigroup Forum 33 (1986), 331–356.Google Scholar
  20. 20.
    F. Otto: Deciding algebraic properties of finitely presented monoids; in: B. Benninghofen, S. Kemmerich, M.M. Richter, Systems of Reductions, Lecture Notes in Computer Science 277 (1987), 218–255.Google Scholar
  21. 21.
    F. Otto: Finite canonical rewriting systems for congruences generated by concurrency relations; Math. Systems Theory 20 (1987), 253–260.Google Scholar
  22. 22.
    C. Squier: Word problems and a homological finiteness condition for monoids; Journal of Pure and Applied Algebra 49 (1987), 201–217.Google Scholar
  23. 23.
    H. Tietze: Uber die topologischen Invarianten mehrdimensionaler Mannigfaltigkeiten; Monatsheft Math. Physik 19 (1908), 1–118.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Friedrich Otto
    • 1
  1. 1.Department of Computer ScienceState University of New YorkAlbanyU.S.A.

Personalised recommendations