Denotational and Algebraic Semantics for Cyber-physical Systems

The cyber-physical system (CPS) is a dynamic system that contains both continuous and discrete behaviors. It has a wide range of applications in fields such as health care equipment, intelligent traffic control and environmental monitoring. However, the combination of continuous physical behavior and discrete control behavior may complicate the design of systems further. It is of great necessity to give an explicit formal language and its semantics for CPS. In this paper, we elaborate the modeling language for CPS based on our previous work. This language supports shared variables to model the interaction between the physical and the cyber. Additionally, we give it denotational semantics and algebraic semantics, especially focus on the continuous behavior and its composition with the discrete behavior. Throughout this paper, we also present some examples to illustrate the feasibility of the language and its semantics.