Sofic-Dyck shifts

We define the class of sofic-Dyck shifts which extends the class of Markov-Dyck shifts introduced by Inoue, Krieger and Matsumoto. Sofic-Dyck shifts are shifts of sequences whose finite factors form unambiguous context-free languages. We show that they correspond exactly to the class of shifts of sequences whose sets of factors are visibly pushdown languages. We give an expression of the zeta function of a sofic-Dyck shift

On subshift presentations

We consider partitioned graphs, by which we mean finite strongly connected directed graphs with a partitioned edge set ${\mathcal E} ={\mathcal E}^- \cup{\mathcal E}^+$. With additionally given a relation $\mathcal R$ between the edges in ${\mathcal E}^-$ and the edges in $\mathcal E^+$, and denoting the vertex set of the graph by ${\frak P}$, we speak of an an ${\mathcal R}$-graph ${\mathcal G}_{\mathcal R}({\frak P},{\mathcal E}^-,{\mathcal E}^+)$. From ${\mathcal R}$-graphs ${\mathcal G}_{\mathcal R}({\frak P},{\mathcal E}^-,{\mathcal E}^+)$ we construct semigroups (with zero) ${\mathcal S}_{\mathcal R}({\frak P}, {\mathcal E}^-,{\mathcal E}^+)$ that we call ${\mathcal R}$-graph semigroups. We describe a method of presenting subshifts by means of suitably structured labelled directed graphs $({\mathcal V}, \Sigma,\lambda)$ with vertex set ${\mathcal V}$, edge set $\Sigma$, and a label map that asigns to the edges in $\Sigma$ labels in an ${\mathcal R}$-graph semigroup ${\mathcal S}_{\mathcal R}({\frak P}, {\mathcal E}^-, {\mathcal E}^-)$. We call the presented subshift an ${\mathcal S}_{\mathcal R}({\frak P}, {\mathcal E}^-, {\mathcal E}^-)$-presentation. We introduce a Property $(B)$ and a Property (c), tof subshifts, and we introduce a notion of strong instantaneity. Under an assumption on the structure of the ${\mathcal R}$-graphs ${\mathcal G}_{\mathcal R}({\frak P},{\mathcal E}^-, {\mathcal E}^-)$ we show for strongly instantaneous subshifts with Property $(A)$ and associated semigroup ${\mathcal S}_{\mathcal R}({\frak P},{\mathcal E}^-,{\mathcal E}^-)$, that Properties $(B)$ and (c) are necessary and sufficient for the existence of an ${\mathcal S}_{\mathcal R}({\frak P}, {\mathcal E}^-,{\mathcal E}^-)$-presentation, to which the subshift is topologically conjugate,Comment: 33 page

Unambiguously coded systems

We study the coded systems introduced by Blanchard and Hansel. We give several constructions which allow one to represent a coded system as a strongly unambiguous one

Sofic-Dyck shifts

no abstrac

Shifts of k-nested sequences

International audienceWe introduce a new class of subshifts of sequences, called k-graph shifts, which expresses nested constraints on k symbols instead of on two symbols like for Dyck shifts. These shifts share many properties with Markov-Dyck shifts but are generally not conjugate to them. We prove that they are conjugate to sofic-Dyck shifts. We give a computation of the multivariate zeta function for this class of shifts