Now let be an adjacency matrix with entries in Using these elements we construct a directed graph with the set of vertices and the set of edges containing the directed edge in if and only if . Let be the set of all infinite admissible sequences of edges, where by admissible it is meant that the sequence is a walk of the graph, and the sequence can be either one-sided or two-sided infinite. Let be the left shift operator on such sequences; it plays the role of the time-evolution operator of the dynamical system. A subshift of finite type is then defined as a pair obtained in this way. If the sequence extends to infinity in only one direction, it is called a one-sided subshift of finite type, and if it is bilateral, it is called a two-sided subshift of finite type.
