Abstract

Hybrid systems model cyber-physical systems as dynamical systems with interacting discrete transitions and continuous evolutions along differential equations. They arise frequently in many application domains, including aviation, automotive, railway, and robotics. We study hybrid games, i.e. games on hybrid systems combining discrete and continuous dynamics. Unlike hybrid systems, hybrid games allow choices in the system dynamics to be resolved adversarially by different players with different objectives.

This talk describes how logic and formal verification can be lifted to hybrid games. The talk describes a logic for hybrid systems called differential game logic dGL. The logic dGL can be used to study the existence of winning strategies for hybrid games. We present a simple sound and complete axiomatization of dGL relative to the fixpoint logic of differential equations. We prove hybrid games to be determined and their winning regions to require higher closure ordinals and we identify separating axioms, i.e. axioms that distinguish hybrid games from hybrid systems.