Abstract
Given a finite special string-rewriting systemR on Σ and a wordw ε Σ*, it is decidable in polynomial time whether or notR is confluent on the congruence class [w] R .
Similar content being viewed by others
References
B. Benninghofen, S. Kemmerich, M. M. Richter,Systems of Reductions, Lecture Notes in Computer Science, Vol. 277, Springer-Verlag, Berlin, 1987.
R. V. Book, Confluent and other types of Thue systems,Journal of the Association for Computing Machinery 29 (1982), 171–182.
R. V. Book, Decidable sentences of Church-Rosser congruences,Theoretical Computer Science 23 (1983), 301–312.
R. V. Book, Thue systems as rewriting systems,Journal of Symbolic Computation 3 (1987), 39–68.
R. V. Book, C. O'Dunlaing, Testing for the Church-Rosser property,Theoretical Computer Science 16 (1981), 223–229.
H. Bücken, Reduction systems and small cancellation theory,Proceedings of the 4th Workshop on Automated Deduction (1979), pp. 53–59.
R. H. Gilman, Presentations of groups and monoids,Journal of Algebra 57 (1979), 544–554.
J. E. Hopcroft, J. D. Ullman,Introduction to Automata Theory, Languages and Computation, Addison-Wesley, Reading, MA, 1979.
M. Jantzen,Confluent String Rewriting, Springer-Verlag, Berlin, 1988.
D. Kapur, M. S. Krishnamoorthy, R. F. McNaughton, P. Narendran, AnO(¦T¦3) algorithm for testing the Church-Rosser property of Thue systems,Theoretical Computer Science 35 (1985), 109–114.
Ph. LeChenadec,Canonical Forms in Finitely Presented Algebras, Pitman, London, Wiley, New York, 1986.
R. C. Lyndon, P. E. Schupp,Combinatorial Group Theory, Springer-Verlag, Berlin, 1977.
K. Madiener, P. Narendran, F. Otto, A specialized completion procedure for monadic string-rewriting systems presenting groups, in: J. Leach Albert, B. Monien, M. Rodriguez Artalejo (eds.),Automata, Languages, and Programming, Proceedings of the 18th International Colloquium, Lecture Notes in Computer Science, Vol. 510, Springer-Verlag, Berlin, 1991, pp. 279–290.
K. Madiener, F. Otto, Using string-rewriting for solving the word problem for finitely presented groups,Information Processing Letters 24 (1987), 281–284.
R. F. McNaughton, P. Narendran, Special monoids and special Thue systems,Journal of Algebra 108 (1987), 248–255.
F. Otto, On deciding the confluence of a finite string-rewriting system on a given congruence class,Journal of Computer and System Sciences 35 (1987), 285–310.
F. Otto, Completing a finite special string-rewriting system on the congruence class of the empty word,Applicable Algebra in Engineering, Communication and Computing, to appear.
F. Otto, L. Zhang, Decision problems for finite special string-rewriting systems that are confluent on some congruence class,Acta Informatica 28 (1991), 477–510.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Otto, F. The problem of deciding confluence on a given congruence class is tractable for finite special string-rewriting systems. Math. Systems Theory 25, 241–251 (1992). https://doi.org/10.1007/BF01213858
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01213858