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A specialized completion procedure for monadic string-rewriting systems presenting groups

  • Rewriting And Logic (Session 7)
  • Conference paper
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Book cover Automata, Languages and Programming (ICALP 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 510))

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Abstract

Based on a simplified test for determining whether a finite monadic string-rewriting system R presenting a group is confluent on [e]R. a procedure for completing a system of this form on [e]R is derived. The correctness and completeness of this procedure are shown.

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References

  1. J.M. Autebert, L. Boasson, G. Senizergues; Groups and NTS languages; J. Comput. System Sci. 35 (1987), 243–267.

    Google Scholar 

  2. R.V. Book; Decidable sentences of Church-Rosser congruences; Theoretical Computer Science 23 (1983), 301–312.

    Google Scholar 

  3. R.V. Book; Thue systems as rewriting systems; J. Symbolic Computation 3 (1987), 39–68.

    Google Scholar 

  4. H. Bücken; Reduction systems and small cancellation theory; in: Proceedings 4th Workshop on Automated Deduction (1979), 53–59.

    Google Scholar 

  5. R.H. Gilman; Presentations of groups and monoids; J. of Algebra 57 (1979), 544–554.

    Google Scholar 

  6. J.E. Hopcroft, J.D. Ullman; Introduction to Automata Theory, Languages and Computation (Addison-Wesley, Reading, MA, 1979).

    Google Scholar 

  7. M. Jantzen. Confluent String-Rewriting (Springer, Berlin, 1988).

    Google Scholar 

  8. D. Kapur, P. Narendran; The Knuth-Bendix completion procedure and Thue systems; SIAM J. on Computing 14 (1985), 1052–1072.

    Google Scholar 

  9. D. Knuth, P. Bendix; Simple word problems in universal algebras; in: J. Leech (ed.), Computational Problems in Abstract Algebra (Pergamon, New York, 1970), 263–297.

    Google Scholar 

  10. Ph. LeChenadec; Canonical Forms in Finitely Presented Algebras (Pitman: London, Wiley: New York, Toronto, 1986).

    Google Scholar 

  11. R.C. Lyndon, P.E. Schupp; Combinatorial Group Theory (Springer, Berlin, 1977).

    Google Scholar 

  12. K. Madlener, F. Otto; Using string-rewriting for solving the word problem for finitely presented groups; Information Processing Letters 24 (1987), 281–284.

    Google Scholar 

  13. K. Madlener, F. Otto; About the descriptive power of certain classes of finite string-rewriting systems; Theoretical Computer Science 67 (1989), 143–172.

    Google Scholar 

  14. K. Madlener, F. Otto; Decidable sentences for context-free groups, in: C. Choffrut, M. Jantzen (eds.) Proceedings of STACS '91, Lecture Notes in Computer Science 480 (1991), 160–171.

    Google Scholar 

  15. K. Madlener, P. Narendran, F. Otto: A specialized completion procedure for monadic string-rewriting systems presenting groups, SEKI-Report SR-90-24. University of Kaiserslautern (1990).

    Google Scholar 

  16. D.E. Muller, P.E. Schupp; Groups the theory of ends, and context-free languages; J. Comput. Systems Ci. 26 (1983), 295–310.

    Google Scholar 

  17. P. Narendran, C. O'Dunlaing, F. Otto; It is undecidable whether a finite special string-rewriting system presents a group: Discrete Math., to appear.

    Google Scholar 

  18. F. Otto; On deciding whether a monoid is a free monoid or is a group; Acta Informatica 23 (1986), 99–110.

    Google Scholar 

  19. F. Otto; On deciding the confluence of a finite string-rewriting system on a given congruence class; J. Comp. Sci. Sciences 35 (1987), 285–310.

    Google Scholar 

  20. F. Otto; 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.

    Google Scholar 

  21. F. Otto; Completing a finite special string-rewriting system presenting a group on the congruence class of the empty word; Preprint No. 8/90, FB Math., GhK, Kassel, West Germany, 1990.

    Google Scholar 

  22. C.C. Squier; Word problems and a homological finiteness condition for monoids, J. Pure Appl. Algebra 49 (1987), 201–217.

    Google Scholar 

  23. L. Zhang; The word problem and undecidability results for finitely presented special monoids; submitted for publication.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Fachbereich Informatik, Universität Kaiserslautern, Postfach 3049, 6750, Kaiserslautern, Germany

    K. Madlener

  2. Department of Computer Science, State University of New York, 1222, Albany, NY, U.S.A.

    P. Narendran

  3. Fachbereich Mathematik-Informatik, Gesamthochschule Kassel, Postfach 101380, 3500, Kassel, Germany

    F. Otto

Authors
  1. K. Madlener
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  2. P. Narendran
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  3. F. Otto
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Editor information

Javier Leach Albert Burkhard Monien Mario Rodríguez Artalejo

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© 1991 Springer-Verlag Berlin Heidelberg

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Madlener, K., Narendran, P., Otto, F. (1991). 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. ICALP 1991. Lecture Notes in Computer Science, vol 510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54233-7_141

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  • DOI: https://doi.org/10.1007/3-540-54233-7_141

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54233-9

  • Online ISBN: 978-3-540-47516-3

  • eBook Packages: Springer Book Archive

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