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Rational ω-transductions

  • M. Latteux
  • E. Timmerman
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 452)

Abstract

The rational ω-transductions (defined by F. Gire as bimorphisms) are particular transductions for infinite words. In this paper we give characterizations of these transductions. On the one hand they coincide with the compositions of non erasing and inverse non erasing morphisms, and only three morphisms are necessary. On the other hand they can be defined from bifaithful rational transductions using a limit operation we call adherence.

Keywords

Rational Adherence Input Alphabet Rational Subset Infinite Path Left Factor 
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]
    D. Beauquier and D. Perrin, "Codeterministic automata on infinite words", Inform. Process. Letters 20 (1985), pp. 95–98.Google Scholar
  2. [2]
    J. Berstel, "Transductions and context-free languages", Teubner 1979, Stuttgart.Google Scholar
  3. [3]
    L. Boasson and M. Nivat, "Sur diverses familles de languages fermées par transduction rationnelle", Acta Informatica 2 (1973), PP. 180–188.Google Scholar
  4. [4]
    L. Boasson and M. Nivat, "Adherences of languages", J. Comput. Syst. Sciences 20 (1980), pp. 285–309.Google Scholar
  5. [5]
    J.R. Büchi, "On a decision method in restricted second order arithmetic", in Proc. 1960 Int.Congr. for Logic, Stanford Univ. Press, pp. 1–11.Google Scholar
  6. [6]
    K. Culik II and J.K. Pachl, "Equivalence problems for mappings on infinite strings", Inform. and Control 49 (1981), pp. 52–53.Google Scholar
  7. [7]
    S. Eilenberg, "Automata, Languages and Machines", vol. A, Academic Press, New York, 1974.Google Scholar
  8. [8]
    C Frougny, "Systèmes de numération linéaires et automates finis", Thèse d'Etat, Paris VII, 1989.Google Scholar
  9. [9]
    F. Gire, "Relations rationnelles infinitaires", Thèse de 3ème cycle, Paris VII, 1981.Google Scholar
  10. [10]
    F. Gire, "Une extension aux mots infinis de la notion de transduction rationnelle", 6th GI conf. (1983), Lecture Notes in Comput. Sci. 145, pp. 123–139.Google Scholar
  11. [11]
    F. Gire and M. Nivat, "Relations rationnelles infinitaires", Calcolo 21 (1984), pp. 91–125.Google Scholar
  12. [12]
    J. Karhumäki and M. Linna, "A note on morphic characterization of languages", Discrete Appl. Math. 5 (1983), pp. 243–246.Google Scholar
  13. [13]
    L.H. Landweber, "Decision problems for ω-automata", Math. Syst. Theory 3 (1969), pp. 376–384.Google Scholar
  14. [14]
    M. Latteux and J. Leguy, "On the composition of morphisms and inverse morphisms", Lecture Notes Comput. Sciences 154 (1983), pp. 420–432.Google Scholar
  15. [15]
    M. Latteux and E. Timmerman, "Two characterizations of rational adherences", T. C. S. 46 (1986), pp. 101–106.Google Scholar
  16. [16]
    M. Latteux and E. Timmerman, "Bifaithful starry transductions", Inform. Process. Letters 28 (1988), PP. 1–4.Google Scholar
  17. [17]
    M. Latteux and E. Timmerman, "Rational ω-transductions", technical report Univ. Lille 1, LIFL no IT 176 (1990).Google Scholar
  18. [18]
    R. McNaughton, "Testing and generating infinite sequences by a finite automaton", Inform. and Control 9 (1966), pp. 521–530.Google Scholar
  19. [19]
    L. Staiger, "Sequential mappings of ω-languages", RAIRO Inf. Theo. et Applic. 21 (1987), pp. 147–173.Google Scholar
  20. [20]
    L. Staiger, "Research in the theory of ω-languages", J. Inf. Process. Cybern. EIK 23 (1987) pp. 415–439.Google Scholar
  21. [21]
    M. Takahashi and H. Yamasaki, "A note on ω-regular languages", T. C. S. 23 (1983), pp. 217–225.Google Scholar
  22. [22]
    E. Timmerman, "The three subfamilies of rational ω-languages closed under ω-transductions", T. C. S. to appear.Google Scholar
  23. [23]
    S. Tison, "Mots infinis et processus. Objets infinitaires et topologie", Thèse de 3ème cycle, Lille 1, 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • M. Latteux
    • 1
  • E. Timmerman
    • 1
  1. 1.Université de Lille 1, LIFLVilleneuve d'Ascq cedexFrance

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