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Effective S-adic Symbolic Dynamical Systems

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Pursuit of the Universal (CiE 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9709))

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Abstract

We focus in this survey on effectiveness issues for S-adic subshifts and tilings. An S-adic subshift or tiling space is a dynamical system obtained by iterating an infinite composition of substitutions, where a substitution is a rule that replaces a letter by a word (that might be multi-dimensional), or a tile by a finite union of tiles. Several notions of effectiveness exist concerning S-adic subshifts and tiling spaces, such as the computability of the sequence of iterated substitutions, or the effectiveness of the language. We compare these notions and discuss effectiveness issues concerning classical properties of the associated subshifts and tiling spaces, such as the computability of shift-invariant measures and the existence of local rules (soficity). We also focus on planar tilings.

This work was supported by ANR DynA3S and QuasiCool. We would like to thank warmly the anonymous referees, M. Rigo and F. Durand for their useful comments.

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Author information

Authors and Affiliations

  1. IRIF, CNRS UMR 8243, Univ. Paris Diderot, Paris, France

    Valérie Berthé

  2. LIPN, CNRS UMR 7030, Univ. Paris 13, Villetaneuse, France

    Thomas Fernique

  3. I2M UMR 7373, Aix Marseille Univ., Marseille, France

    Mathieu Sablik

Authors
  1. Valérie Berthé
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  2. Thomas Fernique
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  3. Mathieu Sablik
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Corresponding author

Correspondence to Valérie Berthé .

Editor information

Editors and Affiliations

  1. Swansea University, Swansea, United Kingdom

    Arnold Beckmann

  2. Université Paris-Diderot - Paris 7, Paris, France

    Laurent Bienvenu

  3. University of South Florida, Tampa, Florida, USA

    Nataša Jonoska

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Berthé, V., Fernique, T., Sablik, M. (2016). Effective S-adic Symbolic Dynamical Systems. In: Beckmann, A., Bienvenu, L., Jonoska, N. (eds) Pursuit of the Universal. CiE 2016. Lecture Notes in Computer Science(), vol 9709. Springer, Cham. https://doi.org/10.1007/978-3-319-40189-8_2

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  • DOI: https://doi.org/10.1007/978-3-319-40189-8_2

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