7 problems

Soficity conjecture. The subshift $H$ is sofic if and only if $H^\ast$ is sofic.

Let $D$ be a labeled graph presenting an irreducible sofic shift. Denote by $(\underline{\mathbb F}(D),L_{\underline{\mathbb F}(D)})$ and…

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…

Guillon–Jeandel conjecture. If a $\mathbb{Z}$-subshift induces to a sofic $\mathbb{Z}^2$-subshift, then the original $\mathbb{Z}$-subshift is sofic.

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…

Let $A$ be an alphabet, let $G\leq\Gamma$ be finitely generated groups, and let ${\mathcal F}$ be a set of patterns with supports contained in $G$. Write…