Composition and Refinement of Discrete Real-Time Systems

Reactive systems exhibit ongoing, possibly non-terminating, interaction with the environment. Real-time systems are reactive systems that must satisfy quantitative timing constraints. This paper presents a structured compositional design method for discrete real-time systems that can be used to combat the combinatorial explosion of states in the verification of large systems. A composition rule describes how the correctness of the system can be determined from the correctness of its modules, without knowledge of their internal structure. The advantage of compositional verification is clear. Each module is both simpler and smaller than the system itself. Composition requires the use of both model-checking and deductive techniques. A refinement rule guarantees that specifications of high-level modules are preserved by their implementations. The StateTime toolset is used to automate parts of compositional designs using a combination of model-checking and simulation. The design method is illustrated using a reactor shutdown system that cannot be verified using the StateTime toolset (due to the combinatorial explosion of states) without compositional reasoning. The reactor example also illustrates the use of the refinement rule.