Abstract
Finite automata on \(\omega\)-sequences and \(\omega\)-trees were introduced in the sixties by Buchi, 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.
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