Formal specification and executable analysis of digital twin systems using Maude rewriting logic

Digital Twins (DTs) are revolutionizing industries by enabling real-time simulation, monitoring, and predictive analysis of physical systems. However, the complexity of DTs and the lack of formal specification frameworks hinder their rigorous analysis and verification, limiting their reliability in critical applications. This article presents a novel formal and executable DT system model based on rewriting logic, leveraging Maude as a high-performance specification and analysis tool. Unlike existing models, which are often either informal, semi-formal, or non-executable, our approach ensures precise syntax, well-defined semantics, and full executability. This approach enables automated verification through reachability analysis, model checking, and theorem proving. Our model captures essential DT functional primitives with abstraction, enabling precise modeling of dynamic behaviors and state transitions. We formally define a structured event-driven DT system architecture, decomposing DT functions into sensing, actuation, processing, and communication layers. The model’s applicability is demonstrated through two case studies: a thermostat system (capturing property-level synchronization) and an incubator system (modeling state-level synchronization). Simulation and verification results reveal critical insights into DT synchronization, showing that initial state discrepancies persist over time, emphasizing the need for formal DT validation techniques. Our rigorous, scalable, and adaptable DT modeling paradigm paves the way for more robust, verifiable, and reliable digital twin applications across industries.