On Automata on infinite trees

In the paper, first of all we analyze new conditions for acceptance of sets of infinite trees recognized by Muller automata and for which equivalent Büchi automata can be given. We define a new model of infinite tree automata, called limited Muller automata, and investigate their characterization in weak monadic logic. In the second part, we extend the notion of control automaton to the case where more than one language is used to control the set of infinite words labeling each path of a successful run on a tree. We prove that using boolean operators in defining acceptance conditions for control automata, a characterization in terms of control automata for M–automata, introduced by Nivat and Saoudi, and other classes of automata can be given. We introduce the And-control automaton and use this notion to prove properties of boolean closure of deterministic classes of automata.