A logic for model-checking mean-field models

Recently the mean-field method has been adopted for analysing systems consisting of a large number of interacting objects in computer science, biology, chemistry, etc. It allows for a quick and accurate analysis of such systems, while avoiding the state-space explosion problem. So far, the method has primarily been used for performance evaluation. In this paper, we use the mean-field method for model-checking. We define and motivate a logic MF-CSL for describing properties of systems composed of many identical interacting objects. The proposed logic allows describing both properties of the overall system and of a random individual object. Algorithms to check the satisfaction relation for all MF-CSL operators are proposed. Furthermore, we explain how the set of all time instances that fulfill a given MF-CSL formula for a certain distribution of objects can be computed.