Recursive Timed Automata

We study recursive timed automata that extend timed automata with recursion. Timed automata, as introduced by Alur and Dill, are finite automata accompanied by a finite set of real-valued variables called clocks. Recursive timed automata are finite collections of timed automata extended with special states that correspond to (potentially recursive) invocations of other timed automata from their collection. During an invocation of a timed automaton, our model permits passing the values of clocks using both pass-byvalue and pass-by-reference mechanisms. We study the natural reachability and termination (reachability with empty invocation stack) problems for recursive timed automata. We show that these problems are decidable (in many cases with the same complexity as the reachability problem on timed automata) for recursive timed automata satisfying the following condition: during each invocation either all clocks are passed by reference or none is passed by reference. Furthermore, we show that for recursive timed automata that violate this condition reachability/termination problems are undecidable for automata with as few as three clocks. We also establish similar results for two-player game extension of our model against reachability/termination objective.