Cyclic languages and strongly cyclic languages

  • Marie -Pierre Béal
  • Olivier Carton
  • Christophe Reutenauer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1046)


We prove that cyclic languages are the boolean closure of languages called strongly cyclic languages. The result is used to give another proof of the rationality of the zeta function of rational cyclic languages.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Béa93]
    Marie-Pierre Béal. Codage symbolique. Masson, 1993.Google Scholar
  2. [Béa95]
    Marie-Pierre Béal. Puissance extérieure d'un automate déterministe, application au calcul de la fonction zêta d'un système sofique. R.A.I.R.O.-Informatique Théorique et Applications, 29(2):85–103, 1995.Google Scholar
  3. [Bow78]
    Rufus Bowen. Symbolic dynamics. In On axiom A diffeomorphism, number 35 in CBMS Reg. Conf. American Mathematical Society, 1978.Google Scholar
  4. [BP84]
    Jean Berstel and Dominique Perrin. Theory of codes. Academic Press, 1984.Google Scholar
  5. [BR90]
    Jean Berstel and Christophe Reutenauer. Zeta functions of formal languages. Trans. Amer. Math. Soc., 321:533–546, 1990.Google Scholar
  6. [Car93]
    Olivier Carton. Mots infinis, ω-semigroupes et topologie. Thèse, Université Paris 7, 1993. Rapport LITP-TH 93-08.Google Scholar
  7. [Eil72]
    S. Eilenberg. Automata, languages and machines, volume A. Academic Press, New York, 1972.Google Scholar
  8. [Lal79]
    Gérard Lallement. Semigroups and combinatorial applications. Wiley, 1979.Google Scholar
  9. [Man71]
    A. Manning. Axiom A diffeomorphisms have rationnal zeta fonctions. Bull. London Math. Soc., 3:215–220, 1971.Google Scholar
  10. [Pin86]
    Jean-Eric Pin. Varieties of formal languages. North Oxford, London and Plenum, New-York, 1986. (Traduction de Variétés de langages formels).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Marie -Pierre Béal
    • 1
  • Olivier Carton
    • 2
  • Christophe Reutenauer
    • 3
  1. 1.LITP - Institut Blaise PascalUniversité Denis DiderotParis cedex 05
  2. 2.Institut Gaspard MongeUniversité de Marne-la-ValléeNoisy le Grand cedex
  3. 3.MathématiquesUniversité du Québec à MontréalMontréalCanada

Personalised recommendations