Terminology
By convention, the term shift is understood to refer to the full n-shift. A subshift is then any subspace of the full shift that is shift-invariant (that is, a subspace that is invariant under the action of the shift operator), non-empty, and closed for the product topology defined below. Some subshifts can be characterized by a transition matrix, as above; such subshifts are then called subshifts of finite type. Often, this distinction is relaxed, and subshifts of finite type are called simply shifts of finite type. Subshifts of finite type are also sometimes called topological Markov shifts.
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