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arXiv · 1401.0705

Undecidable properties of self-affine sets and multi-tape automata

Timo Jolivet·Jarkko Kari
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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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Timo Jolivet, Jarkko Kari. 2014-01-03. Undecidable properties of self-affine sets and multi-tape automata. https://doi.org/10.1007/978-3-662-44522-8_30

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