Undecidable properties of self-affine sets and multi-tape automata
Formal Languages and Automata Theory
2014-09-26 v2 Combinatorics
Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1401.0705,
title = {Undecidable properties of self-affine sets and multi-tape automata},
author = {Timo Jolivet and Jarkko Kari},
journal= {arXiv preprint arXiv:1401.0705},
year = {2014}
}
Comments
10 pages, v2 includes some corrections to match the published version