High Quality Content by WIKIPEDIA articles! In symbolic dynamics and related branches of mathematics, a shift space or subshift is a set of infinite words representing the evolution of a discrete system. In fact, shift spaces and symbolic dynamical systems are often considered synonyms. Let A be a finite set of states. An infinite (respectively bi-infinite) word over A is a sequence mathbf x=(x_n)_{nin M}, where M=mathbb N (resp. M=mathbb Z) and xn is in A for any integer n. The shift operator ? acts on an infinite or bi-infinite word by shifting all symbols to the left, i.e. (sigma(mathbf x))(n)=x_{n+1} for all n. In the following we choose M=mathbb N and thus speak of infinite words, but all definitions are naturally generalizable to the bi-infinite case.

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