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Aperiodicity Measure for Infinite Sequences

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Computer Science - Theory and Applications (CSR 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5675))

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Abstract

We introduce the notion of aperiodicity measure for infinite symbolic sequences. Informally speaking, the aperiodicity measure of a sequence is the maximum number (between 0 and 1) such that this sequence differs from each of its non-identical shifts in at least fraction of symbols being this number. We give lower and upper bounds on the aperiodicity measure of a sequence over a fixed alphabet. We compute the aperiodicity measure for the Thue–Morse sequence and its natural generalization the Prouhet sequences, and also prove the aperiodicity measure of the Sturmian sequences to be 0. Finally, we construct an automatic sequence with the aperiodicity measure arbitrarily close to 1.

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Author information

Authors and Affiliations

  1. Department of Mechanics and Mathematics, Moscow State University, Russia

    Yuri Pritykin & Julya Ulyashkina

  2. Computer Science Department, Princeton University, USA

    Yuri Pritykin

Authors
  1. Yuri Pritykin
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  2. Julya Ulyashkina
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Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, 4 Koptyug av, 630090, Novosibirsk, Russia

    Anna Frid

  2. Sobolev Institute of Mathematics SB RAS, Koptyug av. 4, 630090, Novosibirsk, Russia

    Andrey Morozov

  3. Max Planck Institute for Software Systems, Campus E1 4, 66123, Saarbrücken, Germany

    Andrey Rybalchenko

  4. Lehrstuhl für Theoretische Informatik, Institut für Informatik, Julius-Maximilians-Universität Würzburg, Am Hubland, 97974, Würzburg, Germany

    Klaus W. Wagner

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© 2009 Springer-Verlag Berlin Heidelberg

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Pritykin, Y., Ulyashkina, J. (2009). Aperiodicity Measure for Infinite Sequences. In: Frid, A., Morozov, A., Rybalchenko, A., Wagner, K.W. (eds) Computer Science - Theory and Applications. CSR 2009. Lecture Notes in Computer Science, vol 5675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03351-3_26

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  • DOI: https://doi.org/10.1007/978-3-642-03351-3_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03350-6

  • Online ISBN: 978-3-642-03351-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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