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Asymptotic Subword Complexity

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Languages Alive

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7300))

Abstract

The subword complexity of an infinite word ξ is a function f(ξ,n) returning the number of finite subwords (factors, infixes) of length n of ξ. In the present paper we investigate infinite words for which the set of subwords occurring infinitely often is a regular language. Among these infinite words we characterise those which are eventually recurrent.

Furthermore, we derive some results comparing the asymptotics of f(ξ,n) to the information content of sets of finite or infinite words related to ξ. Finally we give a simplified proof of Theorem 6 of [18].

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Author information

Authors and Affiliations

  1. Institut für Informatik, Martin-Luther-Universität Halle-Wittenberg, von-Seckendorf-Platz 1, 06099, Halle, Germany

    Ludwig Staiger

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  1. Ludwig Staiger
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Editors and Affiliations

  1. Institut für Informatik, Universität Potsdam, August-Bebel-Straße 89, 14482, Potsdam, Germany

    Henning Bordihn

  2. Institut für Informatik, Universität Giessen, Arndtstraße 2, 35392, Giessen, Germany

    Martin Kutrib

  3. Fakultät für Informatik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39016, Magdeburg, Germany

    Bianca Truthe

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Staiger, L. (2012). Asymptotic Subword Complexity. In: Bordihn, H., Kutrib, M., Truthe, B. (eds) Languages Alive. Lecture Notes in Computer Science, vol 7300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31644-9_16

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  • DOI: https://doi.org/10.1007/978-3-642-31644-9_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31643-2

  • Online ISBN: 978-3-642-31644-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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