Foundations for the run-time monitoring of reactive systems fundamentals of the MaC language

As the complexity of systems grows, the correctness of systems becomes harder to achieve. This difficulty promotes a run-time monitoring technique as a promising complementary methodology for higher system assurance. To formalize and understand the computational nature of run-time monitoring is a key to utilize this valuable technique. In this paper, we formalize the notion of run-time monitoring of reactive systems in terms of ω-languages and show that the language of Monitoring and Checking (MaC) architecture, called MEDL, is expressive enough for the run-time monitoring. First, we provide a descriptive theory for the class of monitorable languages and show that this class of languages coincides with the class U i of the Arithmetic hierarchy. Second, we introduce a class of automata with storage that can be used to describe the class of monitorable languages using connections to the Arithmetic hierarchy. Finally, we show that MEDL can express the class of monitorable languages via the correspondence between MEDL and the automata with storage.