We introduce symbolic tree automata as a generalization of finite tree automata with a parametric alphabet over any given background theory. We show that symbolic tree automata are closed under Boolean operations, and that the operations are effectively uniform in the given alphabet theory. This generalizes the corresponding classical properties known for finite tree automata.

Symbolic automata theory lifts classical automata theory to rich alphabet theories. It does so by replacing an explicit alphabet with an alphabet described implicitly by a Boolean algebra. How does this lifting affect the basic algorithms that lay the foundation for modern automata theory and what is the incentive for doing this? We investigate these questions here. In our approach we use state...

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 ...

In this paper, we develop the basic theory of disimulations, a type of relation between two automata which witnesses equivalence. We show that many standard constructions in the theory of automata such as determinization, minimization, inaccessible state removal, et al., are instances of disimilar automata. Then, using disimulations, we define an “algebraic” proof system for the equational theo...

The classical theory of deterministic automata is presented in terms of the notions of homomor-phism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which coinduction proof methods for language equality and language inclusion. At the same time, the p...

Alfaro and Henzinger use alternating simulation in a two player game as a refinement for interface automata [1]. We show that interface automata correspond to a subset of modal transition systems of Larsen and Thomsen [2], on which alternating simulation coincides with modal refinement. As a consequence a more expressive interface theory may be built, by a simple generalization from interface a...

Connections between Tree Automata and Term Rewriting are now well known. Whereas treeautomata can be viewed as a subclass of ground rewrite systems, tree automata are successfullyused as decision tools in rewriting theory. Furthermore, applications, including rewriting theory,have influenced the definition of new classes of tree automata. In this talk, we will first presenta sho...

Connections between Tree Automata and Term Rewriting are now well known. Whereas tree automata can be viewed as a subclass of ground rewrite systems, tree automata are successfully used as decision tools in rewriting theory. Furthermore, applications, including rewriting theory, have influenced the definition of new classes of tree automata. In this talk, we will first present a short and not e...