Definition:One-Sided Shift of Finite Type

Definition
Let $\mathbf A = \sqbrk a_k$ be a logical matrix for a $k \in \Z: k \ge 2$.

Let:
 * $X_\mathbf A ^+ = \set {x = \sequence {x_n}_{n \mathop \in \N} : x_n \in \set {1, 2, \ldots, k}, a_{x_n, x_{n + 1} } = 1}$

Let $\sigma_\mathbf A ^+ : X_\mathbf A ^+ \to X_\mathbf A ^+$ be the forward shift operator, that is:
 * $\map {\sigma _{\mathbf A} ^+ } x := y$

where $y_n = x_{n + 1}$ for all $n \in \N$.

Then the pair $\struct {X _\mathbf A ^+, \sigma_\mathbf A ^+}$ is called a one-sided shift of finite type.