Reachability in timed automata with diagonal constraints

We consider the reachability problem for timed automata having diagonal constraints (like x - y < 5) as guards in transitions. The best algorithms for timed automata proceed by enumerating reachable sets of its configurations, stored in the form of a data structure called "zones". Simulation relations between zones are essential to ensure termination and efficiency. The algorithm employs a simulation test "is-Z-simulated-by-Z' ?" which ascertains that zone Z does not reach more states than zone Z', and hence further enumeration from Z is not necessary. No effective simulations are known for timed automata containing diagonal constraints as guards. In this paper, we propose a simulation relation LU-d for timed automata with diagonal constraints. On the negative side, we show that deciding Z-is-not-LU-d-simulated-by-Z' is NP-complete. On the positive side, we identify a witness for non-simulation and propose an algorithm to decide the existence of such a witness using an SMT solver. The shape of the witness reveals that the simulation test is likely to be efficient in practice.