Some results about confluence on a given congruence class

  • Friedrich Otto
Theoretical Aspects 2
Part of the Lecture Notes in Computer Science book series (LNCS, volume 256)


It is undecidable in general whether or not a term-rewriting system is confluent on a given congruence class. This result is shown to hold even when the term-rewriting systems under consideration contain unary function symbols only, and all their rules are length-reducing. On the other hand, for certain subclasses of these systems confluence on a given congruence class is decidable.


Word Problem Critical Pair Congruence Class Reduction Sequence Pushdown Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    G. Bauer, F. Otto; Finite complete rewriting systems and the complexity of the word problem; Acta Informatica 21 (1984), 521–540.Google Scholar
  2. 2.
    C. Beeri; An improvement on Valiant's decision procedure for equivalence of deterministic finite turn pushdown machines; Theoret. Comput. Sci. 3 (1976), 305–320.Google Scholar
  3. 3.
    R.V. Book; Confluent and other types of Thue systems; Journal ACM 29 (1982), 171–182.Google Scholar
  4. 4.
    R.V. Book; A note on special Thue systems with a single defining relation; Math. Systems Theory 16 (1983), 57–60.Google Scholar
  5. 5.
    H. Buecken; Anwendung von Reduktionssystemen auf das Wortproblem in der Gruppentheorie; dissertation, Aachen, 1979.Google Scholar
  6. 6.
    B. Domanski, M. Anshel; The complexity of Dehn's algorithm for word problems in groups; Journal Algorithms 6 (1985), 543–549.Google Scholar
  7. 7.
    G. Huet, D.S. Lankford; On the uniform halting problem for term rewriting systems; Lab. Rep. No.283, INRIA, Le Chesnay, France, 1978.Google Scholar
  8. 8.
    G. Huet; Confluent reductions: Abstract properties and applications to term rewriting systems; Journal ACM 27 (1980), 797–821.Google Scholar
  9. 9.
    M. Jantzen; A note on a special one-rule semi-Thue system; Inform. 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; Theoret. Comput. Sci. 35 (1985), 337–344.Google Scholar
  11. 11.
    D. Knuth, P. Bendix; Simple word problems in universal algebras; in: J.Leech (ed.), Computational Problems in Abstract Algebra, Pergamon Press, 1970, 263–297.Google Scholar
  12. 12.
    P. LeChenadec; Canonical Forms in Finitely Presented Algebras, Pitman Publ. Limited, John Wiley & Sons, New York, 1986.Google Scholar
  13. 13.
    R.E. Lyndon, P.E. Schupp; Combinatorial Group Theory, Springer, 1977.Google Scholar
  14. 14.
    P. Narendran, C. O'Dunlaing; Cancellativity in finitely presented semigroups; Journal Symbolic Computation, to appear.Google Scholar
  15. 15.
    P. Narendran, C. O'Dunlaing, H. Rolletschek; Complexity of certain decision problems about congruential languages; Journal Comp. System Sciences, 30 (1985), 343–358.Google Scholar
  16. 16.
    C. O'Dunlaing; Finite and infinite regular Thue systems, PhD dissertation, Dept. of Math., University of California, Santa Barbara, 1981.Google Scholar
  17. 17.
    C. O'Dunlaing; Infinite regular Thue systems; Theoret. Comput. Sci. 25 (1983), 171–192.Google Scholar
  18. 18.
    F. Otto; Some undecidability results for non-monadic Church-Rosser Thue systems; Theoret. Comput. Sci. 33 (1984), 261–278.Google Scholar
  19. 19.
    F. Otto; On deciding the confluence of a finite string-rewriting system on a given congruence class; Technical Report 159/86, Fachbereich Informatik, Universitaet Kaiserslautern, 1986; also submitted for publication.Google Scholar
  20. 20.
    L.G. Valiant; The equivalence problem for deterministic finite-turn pushdown automata; Inf. and Control 25 (1974), 123–133.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Friedrich Otto
    • 1
  1. 1.Fachbereich InformatikUniversitaet KaiserslauternKaiserslauternGermany

Personalised recommendations