Topological characterizations of infinite tree languages (Q1092675)

In this paper we define several types of acceptance of finite automata for infinite trees, and study the topological properties of the tree languages accepted thereby. As a consequence, we show that the two classes of tree languages accepted by (nondeterministic) tree automata in the following two types of acceptance coincide: (1) an infinite tree \(\tau\) is accepted iff there is a run for \(\tau\) such that on each path an accepting state is contained; (2) an infinite tree \(\tau\) is accepted iff every run for \(\tau\) contains an accepting state.