Undecidable properties of self-affine sets and multi-tape automata
Timo Jolivet, Jarkko Kari · 2014
We study the decidability of some properties of self-affine sets specified by a graph-directed iterated function system (GIFS) with rational coefficients. We focus on topological properties and we prove that having empty interior is undecidable in dimension two. These results are obtained by studying a particular class of self-affine sets associated with multitape 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. 1