Reachability Games on Recursive Hybrid Automata

Recursive hybrid automata generalize recursive state machines in a similar way as hybrid automata generalize state machines. Recursive hybrid automata can be considered as collection of classical hybrid automata with special states that correspond to potentially recursive invocation of hybrid automata from the collection. During each such invocation, the semantics of recursive hybrid automata permits optional passing of the continuous variables using either pass-by-value or pass-by-reference mechanism. This model generalizes the recursive timed automata model introduced by Trivedi and Wojtczak and dense-timed pushdown automata by Abdulla, Atig, and Stenman. We study two-player turn-based reachability games on recursive hybrid automata. Given the undecidability of even the reachability problem on hybrid automata, it is not surprising that the problems remain undecidable without further restrictions. We consider various restrictions of recursive hybrid automata where we recover decidability of reachability games and characterize the boundaries between decidable and undecidable variants.