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Undecidable Properties of Self-affine Sets and Multi-tape Automata

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Mathematical Foundations of Computer Science 2014 (MFCS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8634))

Abstract

We study the decidability of the topological properties of some objects coming from fractal geometry. We prove that having empty interior is undecidable for the sets defined by two-dimensional graph-directed iterated function systems. These results are obtained by studying a particular class of self-affine sets associated with multi-tape automata. We first establish the undecidability of some language-theoretical properties of such automata, which then translate into undecidability results about their associated self-affine sets.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Turku, Finland

    Timo Jolivet & Jarkko Kari

  2. LIAFA, Université Paris Diderot, France

    Timo Jolivet

Authors
  1. Timo Jolivet
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  2. Jarkko Kari
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Editor information

Editors and Affiliations

  1. Faculty of Informatics, Eötvös Loránd University, Pázmány Péter sétány 1/C, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  2. Fakultät für Informatik und Automatisierung, Technische Universität Ilmenau, Helmholtzplatz, 598693, Ilmenau, Germany

    Martin Dietzfelbinger

  3. Institute of Informatics, Szeged University, Tisza Lajos krt. 103, 6720, Szeged, Hungary

    Zoltán Ésik

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Jolivet, T., Kari, J. (2014). Undecidable Properties of Self-affine Sets and Multi-tape Automata. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_30

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  • DOI: https://doi.org/10.1007/978-3-662-44522-8_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44521-1

  • Online ISBN: 978-3-662-44522-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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