Compositional verification of self-adaptive cyber-physical systems.

Cyber-Physical Systems (CPSs) must often self-adapt to respond to changes in their operating environment. However, using formal verification techniques to provide assurances that critical requirements are satisfied can be computationally intractable due to the large state space of self-adaptive CPSs. In this paper we propose a novel language, Adaptive CSP, to model self-adaptive CPSs modularly and provide a technique to support compositional verification of such systems. Our technique allows system designers to identify (a subset of) the CPS components that can affect satisfaction of given requirements, and define adaptation procedures of these components to preserve the requirements in the face of changes to the system's operating environment. System designers can then use Adaptive CSP to represent the system including potential self-adaptation procedures. The requirements can then be verified only against relevant components, independently from the rest of the system, thus enabling computationally tractable verification. Our technique enables the use of existing formal verification technology to check requirement satisfaction. We illustrate this through the use of FDR, a refinement checking tool. To achieve this, we provide an adequate translation from a subset of Adaptive CSP to the language of FDR. Our technique allows system designers to identify alternative adaptation procedures, potentially affecting different sets of CPS components, for each requirement, and compare them based on correctness and optimality. We demonstrate the feasibility of our approach using a substantive example of a smart art gallery. Our results show that our technique reduces the computational complexity of verifying self-adaptive CPSs and can support the design of adaptation procedures.