Definition:Metric/Shift of Finite Type

Definition
Let $\struct {X _\mathbf A, \sigma_\mathbf A}$ be a shift of finite type.

Let $\theta \in \openint 0 1$.

Then the metric $d_\theta$ on $X _\mathbf A$ is defined by:
 * $\forall x \in X_\mathbf A: \map {d_\theta} {x, x} = 0$

and:
 * $\forall x, y \in X_\mathbf A, x \ne y: \map {d_\theta} {x, y} = \theta ^N$

where:
 * $ N := \max \set {n \in \N : x_i = y_i \text { for all } i \in \openint {-n} n}$

Also see

 * Metric on Shift of Finite Type is Metric
 * Metric on Shift of Finite Type is Non-Archimedean