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Rational cones and commutations

  • Michel Latteux
Chapter 1 Languages
Part of the Lecture Notes in Computer Science book series (LNCS, volume 381)

Abstract

This survey presents some results concerning total commutations, partial commutations and semi-commutations in connection with the families of rational and algebraic languages and more generaly with (faithful) rational cones.

Keywords

Rational Cone Finite Union Letter Alphabet Commutative Monoids Finite Deterministic 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.

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References

  1. [1]
    IJ.J.Aalbersberg and G.Rozenberg, Theory of traces, Tech.Rep., University of Leiden, 1986.Google Scholar
  2. [2]
    IJ.J. Aalbersberg and E. Welzl, Trace languages defined by regular string languages, RAIRO Inform.Theor. 20(1986) 103–119.Google Scholar
  3. [3]
    J.M. Autebert, J. Beauquier, L. Boasson and M. Latteux, Very small families of languages, in R.V. Book,ed., Formal Language Theory, Perspective and Open Problems (Academic Press, New York,1980) 89–107.Google Scholar
  4. [4]
    J.M. Autebert, J. Beauquier, L. Boasson and M. Latteux, Languages algébriques dominés par des languages unaires, Information and Control 48(1981) 49–53.Google Scholar
  5. [5]
    J.Beauquier, M.Blattner and M.Latteux, On commutative context-free languages, J.of Comput. and Syst.Sc. 35(1987).Google Scholar
  6. [6]
    J.Berstel,Transductions and Context-Free Languages (Teubner,1979).Google Scholar
  7. [7]
    J. Berstel and J. Sakarovich, Recent results in the theory of rational sets, Lect.Notes in Comp.Sci. 233(1986) 15–28.Google Scholar
  8. [8]
    A.Bertoni, G.Mauri and N.Sabadini, Unambiguous regular trace languages, in J.Demetrovics, G.Katona and A.Salomaa, eds., Algebra, Combinatorics and Logic in Computer Science (North Holland, 1985).Google Scholar
  9. [9]
    M. Blattner and M. Latteux, Parikh-bounded languages, Lect.Notes in Comp.Sci. 115(1981) 316–323.Google Scholar
  10. [10]
    R.V. Book, S. Greibach and C. Wrathall, Reset machines, J.of Comput. and Syst.Sc. 19(1979) 256–276.Google Scholar
  11. [11]
    P.Cartier and D.Foata, Problèmes combinatoires de commutations et réarrangements, Lect. Notes in Math. 85(1969).Google Scholar
  12. [12]
    M.Clerbout, Commutations partielles et familles de langages, Thesis, University of Lille, 1984.Google Scholar
  13. [13]
    M.Clerbout, Compositions de fonctions de commutation partielle, to appear in RAIRO Inform.Theor., 1986.Google Scholar
  14. [14]
    M. Clerbout and M. Latteux, Partial commutations and faithful rational transductions, Theoretical Computer Science 34(1984) 241–254.Google Scholar
  15. [15]
    M.Clerbout and M.Latteux, On a generalization of partial commutations, in: M.Arato, I.Katai, L.Varga, eds, Proc.Fourth Hung. Computer Sci.Conf. (1985) 15–24.Google Scholar
  16. [16]
    M. Clerbout and M. Latteux, Semi-commutations, Information and Computation 73(1987) 59–74.Google Scholar
  17. [17]
    M.Clerbout and Y.Roos, Semi-communtations algebrico-rationnelles, Tech. Rep. no 126-88, University of Lille, 1988.Google Scholar
  18. [18]
    M.Clerbout and Y.Roos, Semi-commutations et languages algébriques, Tech.Rep. no 129-88, University of Lille, 1988.Google Scholar
  19. [19]
    R.Cori, Partially abelian monoids, Invited lecture, STACS, Orsay, 1986.Google Scholar
  20. [20]
    R.Cori, M.Latteux, Y.Roos and E.Sopena, 2-asynchronous automata, to appear in Theoretical Computer Science, 1987.Google Scholar
  21. [21]
    R. Cori and Y. Metivier, Recognizable subsets of partially abelian monoids, Theoretical Computer Science 38(1985) 179–189.Google Scholar
  22. [22]
    R. Cori and D. Perrin, Automates et commutations partielles, RAIRO Inform.Theor. 19(1985) 21–32.Google Scholar
  23. [23]
    C. Duboc, Some properties of commutation in free partially commutative monoids, Inform.Proc.Letters 20(1985) 1–4.Google Scholar
  24. [24]
    C.Duboc, Commutations dans les monoïdes libres: un cadre théorique pour l'étude du parallélisme, Thesis, University of Rouen, 1986.Google Scholar
  25. [25]
    A. Ehrenfeucht, D. Haussler and G. Rozenberg, Conditions enforcing regularity of context-free languages, Lect.Notes in Comp.Sci. 140(1982) 187–191.Google Scholar
  26. [26]
    S. Eilenberg and M.P. Schützenberger, Rational sets in commutative monoids, J. of Algebra 13(1969) 344–353.Google Scholar
  27. [27]
    S. Ginsburg, The Mathematical Theory of Context-Free Languages (McGraw-Hill, New York,1966).Google Scholar
  28. [28]
    S. Ginsburg, Algebraic and Automata-Theoretic Properties of Formal Languages (North Holland, Amsterdam, 1975).Google Scholar
  29. [29]
    S. Ginsburg and E.H. Spanier, Semigroups, Preburger formulas and languages, Pacif.J.Math. 16(1966) 285–296.Google Scholar
  30. [30]
    S. Ginsburg and E.H. Spanier, AFL with the semilinear property, J.of Comput. and Syst.Sc. 5(1971) 365–396.Google Scholar
  31. [31]
    Ph. Gohon, An algorithm to decide whether a rational subset of Nk is recognizable, Theoretical Computer Science 41(1985) 51–59.Google Scholar
  32. [32]
    A.K. Joshi and T. Yokomori, Semi-linearity,Parikh-boundedness and tree adjunct languages, Inform.Proc.Letters 17(1983) 137–143.Google Scholar
  33. [33]
    J. Kortelainen, On language families generated by commutative languages, Ph.D. Thesis, University of Oulu, 1982.Google Scholar
  34. [34]
    J. Kortelainen, A result concerning the trio generated by commutative slip-languages, Discrete Applied Mathematics 4(1982) 233–236.Google Scholar
  35. [35]
    J. Kortelainen, Every commutative quasirational language is regular, RAIRO Inform.Theor. 20(1986) 319–337.Google Scholar
  36. [36]
    J.Kortelainen, The conjecture of Fliess on commutative context-free languages,to appear, 1988.Google Scholar
  37. [37]
    M. Latteux, Cones rationnels commutativement clos, RAIRO Inform.Theor.11(1977) 29–51.Google Scholar
  38. [38]
    M. Latteux, cones rationnels commutatifs, J.of Comput. and Syst.Sc. 18(1979) 307–333.Google Scholar
  39. [39]
    M. Latteux, Languages commutatifs, transductions rationnelles et intersection, in M.Blab ed., Actes de l'école de printemps de théorie des langages (Tech.Rep.82-14, LITP, 1982) 235–242.Google Scholar
  40. [40]
    M. Latteux and J. Leguy, On the usefulness of bifaifhful rational cones, Math.Systems Theory 18(1985) 19–32.Google Scholar
  41. [41]
    M. Latteux and G. Rozenberg, Commutative one-couter languages are regular, J.of Comput. and Syst.Sc. 29(1984) 54–57.Google Scholar
  42. [42]
    M. Latteux and G. Thierrin, Codes and commutative star languages, Soochow J.of Math. 10(1984) 61–71.Google Scholar
  43. [43]
    H.A. Maurer, The solution of a problem by Ginsburg, Inform.Process.Lett. 1(1971) 7–10.Google Scholar
  44. [44]
    A.Mazurkiewicz, Concurrent program schemes and their interpretations, DAIMI PB 78, University of Aarhus, 1977.Google Scholar
  45. [45]
    A. Mazurkiewicz, Traces, histories and graphs: instances of process monoids, Lect.Notes in Comp.Sci. 176(1984) 115–133.Google Scholar
  46. [46]
    Y.Metivier, Semi commutations dans le monoïde libre,Tech. Rep. n0 I-8606, University of Bordeaux, 1986.Google Scholar
  47. [47]
    Y.Metivier, Contribution à l'étude des monoïdes de commutations,Thèse d'état,University of Bordeaux, 1987.Google Scholar
  48. [48]
    Y. Metivier, On recognizable subsets of free partially commutative monoids, Lect.Notes in Comp.Sci. 226(1986) 254–264.Google Scholar
  49. [49]
    E. Ochmanski, Regular behaviour of concurrent systems, Bulletin of EATCS 27(1985) 56–67.Google Scholar
  50. [50]
    T. Oshiba, On permutting letters of words in context-free languages, Information and Control 20(1972) 405–409.Google Scholar
  51. [51]
    D.Perrin, Words over a partially commutative alphabet, NATO ASI Series F12,Springer (1985) 329–340.Google Scholar
  52. [52]
    J.F. Perrot, Sur la fermeture commutative des C-langages, C.R.Acad.Sci.Paris 265(1967) 597–600.Google Scholar
  53. [53]
    A. Restivo and C. Reutenauer, Rational languages and the Burnside problem, Theoretical Computer Science 40(1985) 13–30.Google Scholar
  54. [54]
    Y.Roos, Virtually asynchronous automata, Conference on Automata, Languages and Programming Systems, Salgotarjan, 1988.Google Scholar
  55. [55]
    Y.Roos, Contribution à l'étude des fonctions de commutation partielle, Thesis, University of Lille, 1989.Google Scholar
  56. [56]
    B.Rozoy, Un modèle de parallélisme: le monoïde distribué, Thèse d'état, University of Caen, 1987.Google Scholar
  57. [57]
    J.Sakarovitch, On regular trace languages, to appear in RAIRO Inform.Theor.Google Scholar
  58. [58]
    A. Salomaa, Theory of Automata, (Pergamon Press, Oxford, 1969).Google Scholar
  59. [59]
    M.Szijarto, The closure of languages on a binary relation, IMYCS Conference, Smolenice,1982.Google Scholar
  60. [60]
    P. Turakainen, On some bounded semiAFLs and AFLs, Inform.Sci. 23(1981) 31–48.Google Scholar
  61. [61]
    W. Zielonka, Notes on asynchronous automata, RAIRO Inform.Theor. 21(1987) 99–135.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Michel Latteux
    • 1
  1. 1.LIFL, CNRS UA 369University of Lille Flandres ArtoisVilleneuve d'Ascq

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