Shift of finite type

In mathematics, subshifts of finite type are used to model dynamical systems, and in particular are the objects of study in symbolic dynamics and ergodic theory. They also describe the set of all possible sequences executed by a finite state machine. The most widely studied shift spaces are the subshifts of finite type.

Let ${\displaystyle V}$ be a finite set of ${\displaystyle n}$ symbols (alphabet). Let X denote the set ${\displaystyle V^{\mathbb {Z} }}$ of all bi-infinite sequences of elements of V together with the shift operator T. We endow V with the discrete topology and X with the product topology. A symbolic flow or subshift is a closed T-invariant subset Y of X and the associated language L_Y is the set of finite subsequences of Y.

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