On the separators on an infinite word generated by a morphism

  • Emmanuelle Garel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 900)

Abstract

Let x be an infinite non periodic word on a finite alphabet A. For each position n, the separator of x at n is the smallest factor of x that starts at n and that does not appear before in x. Denote by Sx(n) the length of the separator of x at n and Sx the corresponding function. We consider the problem of computing Sx in the case where x is generated by iterating some morphism σ: A*→A*. We prove that if σ is q-uniform (q≥2) and x is circular then Sx is q-regular (in the sense of Allouche and Shallit [2], [23]), or, in other words that the corresponding formal power series that associates Sx(n) to the q-ary expression of n is rational (Salomaa, Soittola [22]).

Keywords

Combinatoric on infinite words circularity q-regularity 

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Emmanuelle Garel
    • 1
  1. 1.LITP 4Paris Cedex 05France

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