Abstract Digital twins couple computational models with physical systems to enable services such as predictive reasoning and runtime analysis that support decision–making for maintenance, optimisation and system evolution. They create a technically rich setting for applying formal methods throughout the system lifecycle beyond design-time. This tutorial introduces the elements of digital twin technology, identifying emerging opportunities for formal techniques, including the verification of evolving models under uncertainty, integration of heterogeneous models and rigorous composition of digital twin-enabled systems.

Abstract It is often the case that a robot must adapt to unexpected changes in its environment. It is, however, important that these changes can be demonstrated to maintain the safe operation of the robot. The adaptive systems community has developed the MAPE-K pattern as a widely recognised conceptual architecture. We propose extending MAPE-K to incorporate runtime verification, resulting in an architecture we call MAPLE-K. In this paper, we capture and formalise both the MAPE-K and MAPLE-K architectures using a domain-specific language. Additionally, we provide support for translation from architectural models to software models and code to facilitate the deployment of verified applications. MAPE-K is rarely maintained at the implementation level, but our work ensures traceability between the code and its design, enabling the use of architectural information to verify the correctness of the software.