Verification of Open Systems

In computer system design, we distinguish between closed and open systems. A closed system is a system whose behavior is completely determined by the state of the system. An open system is a system that interacts with its environment and whose behavior depends on this interaction. The ability of temporal logics to describe an ongoing interaction of a reactive program with its environment makes them particularly appropriate for the specification of open systems. Nevertheless, model-checking algorithms used for the verification of closed systemsare not appropriate for the verification of open systems. Correct verification of open systems should check the systemwith respect to arbitrary environments and should take into account uncertainty regarding the environment. This is not the casewith current model-checking algorithms and tools. Module checking is an algorithmic method that checks, given an open system (modeled as a finite structure) and a desired requirement (specified by a temporal-logic formula), whether the open system satisfies the requirement with respect to all environments. In this paper we describe and examine module checking problem, and study its computational complexity. Our results show that module checking is computationally harder than model checking.