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On the separators on an infinite word generated by a morphism

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STACS 95 (STACS 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 900))

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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 S x(n) the length of the separator of x at n and S x the corresponding function. We consider the problem of computing S x 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 S x is q-regular (in the sense of Allouche and Shallit [2], [23]), or, in other words that the corresponding formal power series that associates S x(n) to the q-ary expression of n is rational (Salomaa, Soittola [22]).

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Authors and Affiliations

  1. LITP 4, Place Jussieu, 75252, Paris Cedex 05, France

    Emmanuelle Garel

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  1. Emmanuelle Garel
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Ernst W. Mayr Claude Puech

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© 1995 Springer-Verlag Berlin Heidelberg

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Garel, E. (1995). On the separators on an infinite word generated by a morphism. In: Mayr, E.W., Puech, C. (eds) STACS 95. STACS 1995. Lecture Notes in Computer Science, vol 900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59042-0_67

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  • DOI: https://doi.org/10.1007/3-540-59042-0_67

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59042-2

  • Online ISBN: 978-3-540-49175-0

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