Computing accumulated delays in real-time systems

We present a verification algorithm for duration properties of finite-state real-time systems. While simple real-time properties constrain the total elapsed time between events, duration properties constrain the accumulated time during which certain state predicates hold. We formalize the concept of durations by introducing duration measures for (dense-time) timed automata. Given a timed automaton with a duration measure, a start and a target state, and a duration constraint, the duration-bounded reachability problem asks if there is a run of the automaton from the start state to the target state such that the accumulated duration along the run satisfies the constraint. Our main result is a novel decision procedure for solving the duration-bounded reachability problem. We also prove that the problem is PSPACE-complete and demonstrate how the solution can be used to verify interesting duration properties of real-time systems.