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The Lempel-Ziv Complexity of Fixed Points of Morphisms

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Mathematical Foundations of Computer Science 2006 (MFCS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4162))

Abstract

The Lempel–Ziv complexity is a fundamental measure of complexity for words, closely connected with the famous LZ77, LZ78 compression algorithms. We investigate this complexity measure for one of the most important families of infinite words in combinatorics, namely the fixed points of morphisms. We give a complete characterisation of the complexity classes which are Θ(1), Θ(logn), and Θ(n \(^{\rm 1/{\it k}}\)), k ∈ ℕ, k ≥2, depending on the periodicity of the word and the growth function of the morphism. The relation with the well-known classification of Ehrenfeucht, Lee, Rozenberg, and Pansiot for factor complexity classes is also investigated. The two measures complete each other, giving an improved picture for the complexity of these infinite words.

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Authors and Affiliations

  1. Department of Computer Science, University of Western Ontario, London, Ontario, N6A 5B7, Canada

    Sorin Constantinescu & Lucian Ilie

Authors
  1. Sorin Constantinescu
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  2. Lucian Ilie
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Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynská dolina, 84248, Bratislava, Slovakia

    Rastislav Královič

  2. Institute of Informatics, University of Warsaw, Poland

    Paweł Urzyczyn

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Constantinescu, S., Ilie, L. (2006). The Lempel-Ziv Complexity of Fixed Points of Morphisms. In: Královič, R., Urzyczyn, P. (eds) Mathematical Foundations of Computer Science 2006. MFCS 2006. Lecture Notes in Computer Science, vol 4162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821069_25

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  • DOI: https://doi.org/10.1007/11821069_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37791-7

  • Online ISBN: 978-3-540-37793-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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