We propose a fibred monoidal closed category of alternating tree automata, based on a Dialectica-like approach to the fibred game model of [17]. Alternating tree automata are equivalent in expressive power to the Monadic Second-Order Logic on infinite trees (MSO), which subsumes most of the logics used in verification (see e.g. [14, 5]). Acceptance of an input tree t by an automaton A can be de...

For deterministic tree automata, classical hierarchies, like MostowskiRabin (or index) hierarchy, Borel hierarchy, or Wadge hierarchy, are known to be decidable. However, when it comes to non-deterministic tree automata, none of these hierarchies is even close to be understood. Here we make an attempt in paving the way towards a clear understanding of tree automata. We concentrate on the class ...

We introduce a new syntax-directed translation device called top-down treeto-graph transducer. Such transducers are very similar to the usual top-down tree trans ducers except that the right-hand sides of their rules are hypergraphs rather than trees. Since we are aiming at a device which also allows to translate trees into objects ditTerent from graphs, we focus our attention on so-called tree...

Finite graphs constitute an important tool in various fields of computer science. In order to transfer the theory of finite graphs at least partially to infinite systems, a finite representation of infinite systems is needed. Rewriting systems form a practical model for the finite representation of infinite graphs. Among attractive subclasses of rewriting systems is the class of ground tree rew...

Tree automata based algorithms are essential in many fields in computer science such as verification, specification, program analysis. They become also essential for databases with the development of standards such as XML. In this paper, we define new classes of non deterministic tree automata, namely residual finite tree automata (RFTA). In the bottom-up case, we obtain a new characterization ...