Automata on Inifinite Trees

This article presents the basic theory of automata on infinite trees. We introduce the standard model of nondeterministic automata and the generalization to alternating automata. The central part of the theory considers the closure properties of tree languages definable by such automata, the equivalence of the different models, and their algorithmic properties. We show how these results are obtained and how games of infinite duration can be used as a powerful tool to obtain transparent proofs and algorithms. We also present some applications of tree automata in logic, in particular decidability results and characterizations for monadic second-order logic over infinite trees, and algorithms for the modal μ-calculus.