Zeta functions of recognizable languages

  • Jean Berstel
  • Christophe Reutenauer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 317)


Motivated by symbolic dynamics and algebraic geometry over finite fields, we define cyclic languages and the zeta function of a language. The main result is that the zeta function of a cyclic language which is recognizable by a finite automaton is rational.


Zeta Function Finite Field Finite Automaton Irreducible Polynomial Symbolic Dynamic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Jean Berstel
    • 1
  • Christophe Reutenauer
    • 1
  1. 1.LITPParis

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