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Composition of two semi commutations

  • Y. Roos
  • P. A. Wacrenier
Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 520)

Abstract

We give a decidable necessary and sufficient condition on two semi commutations θ1, θ2 such that the composition of \(f_{\theta _1 }\) and \(f_{\theta _2 }\) is a semi commutation function. This characterization uses the commutation graphs of θ1 and θ2, and the non commutation graphs of θ1 and θ 2 −1 . Then we deduce a decidable graphic characterization of confluent semi commutations.

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References

  1. [1]
    IJ.J. Aabersberg & G. Rozenberg. Theory of Traces. The. Comp. Sci. 60 (1986) 1–83.Google Scholar
  2. [2]
    J. Berstel & J. Sakarovich. Recents results in the theory of rational sets. Lect. Notes in Comp. Sci. 233 (1986) 15–28.Google Scholar
  3. [3]
    P.Cartier & D.Foata. Problèmes combinatoires de commutations et réarrangements. Lect. Notes in Math. 85 (1969).Google Scholar
  4. [4]
    M.Clerbout. Commutations partielles et familles de langages. Thèse Lille, 1984.Google Scholar
  5. [5]
    M. Clerbout & M. Latteux. Partial commutations and faithful rational transductions. The. Comp. Sci. 34 (1984) 241–254.Google Scholar
  6. [6]
    M.Clerbout & M.Latteux. On a generalization of partial commutations. in M.Arato, I.Katai, L.varga, eds, Prc.Fourth Hung. Computer Sci.Conf (1985) 15–24.Google Scholar
  7. [7]
    M. Clerbout & M. Latteux. Semi-commutations. Information and Computation 73 (1987) 59–74.Google Scholar
  8. [8]
    M. Clerbout. Compositions de fonctions de commutation partielle. RAIRO Inform. Theor. 23 (1986) 395–424.Google Scholar
  9. [9]
    M. Clerbout, M. Latteux & Y. Roos. Decomposition of partial commutations. ICALP'90 Lect. Notes in Comp. Sci. 443 (1990) 501–511.Google Scholar
  10. [10]
    M. Clerbout & D. Gonzalez. Decomposition of semi commutations. MFCS'90 Lect. Notes in Comp.Sci. 452 (1990) 209–216.Google Scholar
  11. [11]
    R. Cori & D. Perrin. Automates et commutations partielles. RAIRO Inform. Theor. 19 (1985) 21–32.Google Scholar
  12. [12]
    R. Cori. Partially abelian monoids. Invited lecture, STACS, Orsay (1986).Google Scholar
  13. [13]
    V.Diekert Combinatorics on Traces. Lect. Notes in Comp. Sci. 454 (1990)Google Scholar
  14. [14]
    V.Diekert, E.Ochmanski & K.Reinhardt. On confluent semi commutation systems — decidability and complexity results. To appear (ICALP'91).Google Scholar
  15. [15]
    M.Latteux. Rational cones and commutations. Machines, Languages and Complexity. J.Dassow and J.Kelemen eds., Lect. Notes in Comp.Sci. (1989) 37–54.Google Scholar
  16. [16]
    A.Mazurkiewicz. Concurrent program schemes and their interpretations. DAIMI PB 78, University of Aarhus (1977).Google Scholar
  17. [17]
    A. Mazurkiewicz. Traces, histories and graphs: instances of process monoids. Lect. Notes in Comp.Sci. 176 (1984) 115–133.Google Scholar
  18. [18]
    Y. Metivier. On recognizable subsets of free partially commutative monoids. Lect. Notes in Comp.Sci. 226 (1986) 254–264.Google Scholar
  19. [19]
    E. Ochmanski. Regular behaviour of concurrent systems. Bulletin of EATCS 27 (1985) 56–67.Google Scholar
  20. [20]
    D. Perrin. Words over a partially commutative alphabet. NATO ASI Series F12, Springer (1985) 329–340.Google Scholar
  21. [21]
    Y.Roos. Contribution à l'étude des fonctions de commutations partielles. Thèse, Université de Lille (1989).Google Scholar
  22. [22]
    W. Zielonka. Notes on asynchronous automata. RAIRO Inform. Theor. 21 (1987) 99–135.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Y. Roos
    • 1
  • P. A. Wacrenier
    • 1
  1. 1.CNRS URA 369, L.I.F.L. Université de Lille 1 U.F.R. I.E.E.A. InformatiqueVilleneuve d'Ascq cedex

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