3 problems

Let $S \subset D_2^{\mathbb{N}}$ be a sofic system with primitive adjacency matrix. Let $X$ be the associated self-affine fractal, and say that $S$ has uniform complexity when the…

Let $X$ be a subshift, meaning a closed, shift-invariant subset of $A^{\mathbb{Z}}$ for a finite set $A$. For each $n$, let $F_X(n)$ be the set of distinct follower sets of words o…

Let $A$, $G$, $\Gamma$, and $J$ satisfy the hypotheses of Lemma, and let $\iota_J:A^G\to A^\Gamma$ denote the induction operation. A subshift $X\subseteq A^G$ is sofic if it is the…