During the reporting period, the project has focused on developing theoretical, algorithmic, and data-driven methods for the synthesis and verification of stochastic cyber-physical systems under uncertainty, in line with the objectives of the action. The work performed has advanced abstraction-based control design, robust synthesis under epistemic and aleatoric uncertainty, learning-enabled verification, and scalable methods for stochastic systems, while also establishing software tools to support these developments.
A central activity has been the development of **abstraction-based methods for stochastic systems**, enabling the construction of finite models and controllers with formal probabilistic guarantees. Progress has been achieved on learning abstractions from data, robust abstraction under uncertainty, and multi-objective synthesis for temporal logic specifications. These activities address core scientific goals of the project and provide a foundation for correct-by-design control of complex stochastic systems.
The project has also advanced **learning-enabled verification and certification methods**, including approaches for learning safety and performance certificates from data while maintaining formal guarantees. These developments strengthen the integration between machine learning and formal synthesis and enable verification in settings where accurate system models are not available.
Another key strand of work concerns **robust simulation relations and compositional abstraction-based synthesis**, which support scalable analysis and controller design for large and interconnected stochastic systems. These methods enable reasoning about uncertain systems through structured abstractions and provide the basis for compositional design and verification workflows.
In parallel with theoretical developments, the project has implemented **software tools** that operationalise the proposed methodologies. The LUCID tool supports learning-enabled certification and uncertainty-aware analysis of stochastic dynamical systems, while the SySCoRe toolset supports robust abstraction and formal synthesis for continuous-state stochastic systems. These tools facilitate experimentation, reproducibility, and methodological transfer.
The main scientific achievements to date include:
* robust abstraction and simulation techniques under epistemic uncertainty;
* advances in temporal logic synthesis and certificate-based reasoning;
* the development of data-driven abstraction methods with formal guarantees;
* learning-based construction of certificates for verification and synthesis;
* scalable methods and tool-supported implementations for stochastic systems.
Overall, the work performed during this reporting period has established a coherent methodological foundation for abstraction-based, learning-enabled, and robust synthesis of stochastic cyber-physical systems, positioning the project for further integration of theoretical advances, tool development, and application-driven validation in the next phase.
