Sibilla: A Comprehensive framework for stochastic system analysis and parameter synthesis

Modern technological systems are becoming increasingly complex, with numerous components that interact and adapt their behaviour based on their environment and the actions of other elements. These systems can be found in various domains, from smart cities and autonomous vehicle networks to biological and social networks. The challenge of understanding, analysing, and optimising such systems is significant, as their behaviour emerges from countless local interactions that can be difficult to predict and control. This dissertation addresses these challenges by developing and enhancing an analysis framework that combines statistical methods, surrogate-based optimisation, and formal verification techniques. The research focuses on three fundamental aspects: finding optimal system parameters, verifying system properties, and comparing differ- ent system variants. The proposed approach introduces several methods for system analysis, particularly in the realm of parameter optimisation. Integrating machine learning techniques with statistical verification methods provides efficient ways to explore large parameter spaces and understand their impact on system behaviour. The research demonstrates the framework’s broad applicability through several case studies. These include the analysis of epidemiological models, where the framework helps identify optimal intervention strategies; the study of synthetic biological circuits, where it aids in understanding complex cellular behaviours; and the investigation of consensus protocols, where it helps evaluate different approaches to achieving agree- ment in distributed systems. A significant contribution of this work is the development of methods for systematically comparing different system versions to observe how modifications affect its behaviour, supporting the exploration of alternative designs. This work represents a step forward in understanding and improving complex adaptive systems. While significant challenges remain, the foundations laid here provide a robust platform for future developments in both theoretical understanding and practi- cal applications. The continuing evolution of complex systems in critical applications underscores the importance of further research in this direction.