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

  • Timo Jolivet
  • Jarkko Kari
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8634)


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.


Topological Property Fractal Geometry Iterate Function System Nonempty Interior Empty Interior 
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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2014

Authors and Affiliations

  • Timo Jolivet
    • 1
    • 2
  • Jarkko Kari
    • 1
  1. 1.Department of MathematicsUniversity of TurkuFinland
  2. 2.LIAFAUniversité Paris DiderotFrance

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