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On Critical Exponents in Fixed Points of Binary k-Uniform Morphisms

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STACS 2006 (STACS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3884))

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Abstract

Let w be an infinite fixed point of a binary k-uniform morphism f, and let E(w) be the critical exponent of w. We give necessary and sufficient conditions for E(w) to be bounded, and an explicit formula to compute it when it is. In particular, we show that E(w) is always rational. We also sketch an extension of our method to non-uniform morphisms over general alphabets.

MSC: 68R15.

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Author information

Authors and Affiliations

  1. School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Dalia Krieger

Authors
  1. Dalia Krieger
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Editor information

Editors and Affiliations

  1. LIF, CNRS & Univ. de Provence,, Marseille, France

    Bruno Durand

  2. RWTH Aachen University,, Lehrstuhl Informatik 7,, 52056,, Aachen,, Germany

    Wolfgang Thomas

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© 2006 Springer-Verlag Berlin Heidelberg

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Krieger, D. (2006). On Critical Exponents in Fixed Points of Binary k-Uniform Morphisms. In: Durand, B., Thomas, W. (eds) STACS 2006. STACS 2006. Lecture Notes in Computer Science, vol 3884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11672142_7

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  • DOI: https://doi.org/10.1007/11672142_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32301-3

  • Online ISBN: 978-3-540-32288-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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