On Verification of Linear Occurrence Properties of Real-Time Systems

Duration Calculus of Weakly Monotonic Time (WDC) is an extension of DC to allow description of discrete processes where several steps of computation can occur at the same time point. In this paper, we introduce Linear Occurrence Invariants (LOI) using WDC and give an algorithm to check real-time automata for LOI by solving integer programming problems. LOI can be used effectively to specify system requirements in some cases including when the system is considered under the true synchrony assumption. We also extend WDC probabilistically to express dependability requirements of real-time systems and develop a technique to check deterministic probabilistic real-time automata for a class of probabilistic WDC formulas.