Computing Accumulated Delays in Real-time Systems

We present a veri cation algorithm for duration properties of real-time systems. While simple real-time properties constrain the total elapsed time between events, duration properties constrain the accumulated satisfaction time of state predicates. We formalize the concept of durations by introducing duration measures for timed automata. A duration measure assigns to each nite run of a timed automaton a real number |the duration of the run| which may be the accumulated satisfaction time of a state predicate along the run. Given a timed automaton with a duration measure, an initial and a nal state, and an arithmetic constraint, the duration-bounded reachability problem asks if there is a run of the automaton from the initial state to the nal state such that the duration of the run satis es the constraint. Our main result is an (optimal) Pspace decision procedure for the duration-bounded reachability problem.