Abstract
Based on a polynomial-time test for determining whether a finite special string-rewriting systemR ise-confluent, a procedure for completing a finite special systemR on[e] R is derived. The correctness and completeness of this procedure are proved. In addition, the special case of finite special string-rewriting systems presenting groups is considered.
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References
Book, R. V.: Decidable sentences of Church-Rosser congruences. Theor. Comput. Sci.23, 301–312 (1983)
Cochet, Y.: Church-Rosser congruences on free semigroups. In: Algebraic Theory of Semigroups. Colloquia Mathematica Societatis Janos Bolyai20, pp. 51–60. Amsterdam: North-Holland 1976
Kapur, D., Narendran, P.: The Knuth-Bendix completion procedure and Thue systems. SIAM J. Comput.14, 1052–1072 (1985)
LeChenadec, Ph.: Canonical Forms in Finitely Presented Algebras. London: Pitman, New York, Toronto: Wiley 1986
Lyndon, R. C., Schupp, P. E.: Combinatorial group theory. Berlin, Heidelberg, New York: Springer 1977
Madlener, K., Otto, F.: About the descriptive power of certain classes of finite string-rewriting systems. Theor. Comput. Sci.67, 143–172 (1989)
Madlener, K., Narendran, P., Otto, F.: A specialized completion procedure for monadic string-rewriting systems presenting groups. In: Albert, J. L., Monien, B., Artalejo, M. R. (eds.) Automata, Languages, and Programming. Proceedings of the 18th Int. Coll, Lecture Notes Computer Science, Vol. 510, pp. 279–290. Berlin, Heidelberg, New York: Springer 1991
Narendran, P., O'Dunlaing, C., Otto, F.: It is Undecidable Whether a Finite Special String-Rewriting System Presents a Group. Discrete Math, (to appear)
O'Dunlaing, C.: Finite and Infinite Regular Thue Systems; Ph.D. Dissertation, Department of Mathematics, University of California at Santa Barbara (1981)
Otto, F.: On deciding the confluence of a finite string-rewriting system on a given congruence class. J. Comp. Sys. Sci.35, 285–310 (1987)
Otto, F.: The problem of deciding confluence on a given congruence class is tractable for finite special string-rewriting systems. Preprint No. 4/90, FB Math., GhK Kassel, West Germany (1990); also: Math. Systems Theory (to appear)
Otto, F., Zhang, L.: Decision problems for finite special string-rewriting systems that are confluent on a given congruence class. Acta Informatica28, 477–510 (1991)
Zhang, L.: Conjugacy in special monoids. J. Algebra143, 487–497 (1991)
Zhang, L.: The word problem and Markov properties for finitely presented special monoids. Submitted for publication
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Otto, F. Completing a finite special string-rewriting system on the congruence class of the empty word. AAECC 2, 257–274 (1992). https://doi.org/10.1007/BF01614148
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DOI: https://doi.org/10.1007/BF01614148