We present an efficient algorithm to reduce the size of nondeterministic tree automata, while retaining their language. It is based on new transition pruning techniques, and quotienting of the state space w.r.t. suitable equivalences. It uses criteria based on combinations of downward and upward simulation preorder on trees, and the more general downward and upward language inclusions. Since tr...

We investigate rational relations over trees. Our starting point is the definition of rational tree relations via rational expressions by Raoult (Bull. Belg.Math. Soc. 1997). We develop a new class of automata, called asynchronous tree automata, which recognize exactly these relations. The automata theoretic approach is convenient for the solution of algorithmic problems (like the emptiness pro...

The theory of tree automata was established in the late sixties by Thatcher and Wright [53] and Doner [19]. They showed that the basic logical and algorithmic properties of standard automata theory can be transferred from the domain of finite words to the domain of finite trees (or terms), leading to a theory of regular tree languages. Quoting from the introduction of [53], where the theory of ...

This is a reissue of the book Tree Automata by F. G\'ecseg and M. Steinby originally published in 1984 by Akad\'emiai Kiad\'o, Budapest. Some mistakes have been corrected and a few obscure passages have been clarified. Moreover, some more recent contributions and current lines of research are reviewed in an appendix that also contains several new references.