Formal Verification of Emergent Properties

Complex systems and systems of systems (SoS) are systems characterized by the interconnection of a large number of components or sub-systems. The complexity of such systems increases with the number of components and their manner of connectivity.The global behavior of complex systems and SoS exhibits some properties that cannot be predicted by analysing components or sub-systems in isolation. The verification of these properties called "emergent properties" is considered a crucial issue when engineering such systems. The purpose of this paper is to give an overview and to verify emergent properties. In a first step, we have taken the blinker and the traffic light of the game of life as examples to verify emergence by using the refinement techniques; in a second step, since the refinement is not straightforward, we have taken another example, the Boids model, and by using timed automata and UPPAAL model checking techniques, we have been able to simulate and to verify the emergent properties.