Nested Timed Automata with Invariants

Invariants are usually adopted into timed systems to constrain the time passage within each control location. It is well-known that a timed automaton with invariants can be encoded to an equivalent one without invariants. When recursions are taken into consideration, few results show whether invariants affect expressiveness. This paper investigates the effect of invariants to Nested Timed Automata (NeTAs), a typical real-timed recursive system. In particular, we study the reachability problem for NeTA-Is, which extend NeTAs with invariants. It is shown that the reachability problem is undecidable on NeTA-Is with a single global clock, while it is decidable when no invariants are given. Furthermore, we also show that the reachability is decidable if the NeTA-Is contains no global clocks by showing that a good stack content still satisfies well-formed constraints.