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Growth of Power-Free Languages over Large Alphabets

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Computer Science – Theory and Applications (CSR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6072))

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Abstract

We study growth properties of power-free languages over finite alphabets. We consider the function α(k,β) whose values are the exponential growth rates of β-power-free languages over k-letter alphabets and clarify its asymptotic behaviour. Namely, we suggest the laws of the asymptotic behaviour of this function when k tends to infinity and prove some of them as theorems. In particular, we obtain asymptotic formulas for α(k,β) for the case β ≥ 2.

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Authors and Affiliations

  1. Ural State University,  

    Arseny M. Shur

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  1. Arseny M. Shur
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Editors and Affiliations

  1. Dept. of Theoretical Cybernetics, Kazan State University, 420008, Kazan, Russia

    Farid Ablayev

  2. Institut für Informatik, Technische Universität München, 85748, Garching, Germany

    Ernst W. Mayr

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Shur, A.M. (2010). Growth of Power-Free Languages over Large Alphabets. In: Ablayev, F., Mayr, E.W. (eds) Computer Science – Theory and Applications. CSR 2010. Lecture Notes in Computer Science, vol 6072. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13182-0_35

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  • DOI: https://doi.org/10.1007/978-3-642-13182-0_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13181-3

  • Online ISBN: 978-3-642-13182-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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