Rajeev Alur, Costas Courcoubetis, and Thomas A. Henzinger
We present a verification 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 finite 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 final 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 final state such that the duration of the run satisfies the constraint. Our main result is an (optimal) PSPACE decision procedure for the duration-bounded reachability problem.
Formal Methods in System Design 11:137-156, 1997. A preliminary version appeared in the Proceedings of the Fifth International Conference on Computer-Aided Verification (CAV), Lecture Notes in Computer Science 697, Springer, 1993, pp. 181-193.