Two Approaches to Modelling Logical Time in Cyber-Physical Systems

The paper is devoted to problems caused by the nonlinearity of logical time in distributed, especially cyber-physical, systems. Two approaches to the modelling of such systems are considered in the paper. The operational approach is based on the traditional model that defines the admissible system behaviour as a set of acceptable schedules of the system. The paper argues in favour of restricting possible sets of schedules by that sets of schedules that satisfy certain safety properties. The denotational approach is stated in the language of category theory. This abstraction level clarifies concepts used in the models. In particular, it is explained the feature of linear models as terminal objects with respect to some natural class of morphisms. Further, the interrelation between these two approaches is represented as a formal relation and discuss some properties of the relation that need to be studied.