Verification and synthesis of co-simulation algorithms subject to algebraic loops and adaptive steps

Simulation-based analyses are becoming increasingly vital for the development of cyber-physical systems. Co-simulation is one such technique, enabling the coupling of specialized simulation tools through an orchestration algorithm. The orchestrator describes how to coordinate the simulation of multiple simulation tools. The simulation result depends on the orchestration algorithm that must stabilize algebraic loops, choose the simulation resolution, and adhere to each simulation tool's implementation. This paper describes how to verify that an orchestration algorithm respects all contracts related to the simulation tool's implementation and how to synthesize such tailored orchestration algorithms. The approaches work for complex and adaptive co-simulation scenarios and have been applied to several real-world case studies.