Efficient Model Checking for Duration Calculus Based on Branching-Time Approximations

Duration Calculus (abbreviated to DC) is an interval-based, metric-time temporal logic designed for reasoning about embedded real-time systems at a high level of abstraction. But the complexity of model checking any decidable fragment featuring both negation and chop, DC´s only modality, is non-elementary and thus impractical. We here investigate a similar approximation as frequently employed in model checking situation-based temporal logics, where linear-time problems are safely approximated by branching-time counterparts amenable to more efficient model-checking algorithms. Mimicking the role that a situation has in (A)CTL as origin of a set of linear traces, we define a branching-time counterpart to interval-based temporal logics building on situation pairs spanning sets of intervals. While this branching-time interval semantics yields the desired reduction in complexity of the model-checking problem, from non-elementary to linear in the size of the formula and cubic in the size of the model, the approximation is too coarse to be practical. We therefore refine the semantics by an occurrence count for crucial states (e.g., cuts of loops) in the model, arriving at a 4-fold exponential model-checking problem sufficiently accurately approximating the original one.