Tree Automata: Finite Successes and Infinite Failures

In this section we apply the realization theory of Section 2 to a class of systems in Set which have proved very important in computer science: the tree automata. Since the study of tree automata plays no role in the study of reachability and observability conditions in Section 4 (and only a partial role in Section 5), many control theorists may wish to omit this section unless they have an interest in theory of computation. (An overview of applications is given in Chapter 4 of [7]).