Model Checking Timed Automata with One or Two Clocks

In this paper, we study model checking of timed automata (TAs), and more precisely we aim at finding efficient model checking for subclasses of TAs. For this, we consider model checking TCTL and TCTL ≤,≥ over TAs with one clock or two clocks.First we show that the reachability problem is NLOGSPACE-complete for one clock TAs (i.e. as complex as reachability in classical graphs) and we give a polynomial time algorithm for model checking TCTL ≤,≥ over this class of TAs. Secondly we show that model checking becomes PSPACE-complete for full TCTL over one clock TAs. We also show that model checking CTL (without any timing constraint) over two clock TAs is PSPACE-complete and that reachability is NP-hard.