Timed tree automata with an application to temporal logic

Abstract.

Finite automata on $\omega$-sequences and $\omega$-trees were introduced in the sixties by Büchi, McNaughton and Rabin. Finite automata on timed $\omega$-sequences were introduced by Alur and Dill. In this paper we extend the theory of timed $\omega$-sequences to $\omega$-trees. The main motivation is the introduction of a new way to specify real-time systems and to study, using automata-theoretic techniques, branching-time temporal logics with timing constraints. We study closure properties and decision problems for the obtained classes of timed $\omega$-tree languages. In particular, we show the decidability of the emptiness problem. As an application of the introduced theory, we give a new decidable branching time temporal logic (STCTL) whose semantics is based upon timed $\omega$-trees.