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. This talk studies 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, i.e. ways of resolving the player’s choices in some way so that he wins by achieving his objective for all choices of the opponent. Hybrid games are determined, i.e. one player has a winning strategy from each state, yet their winning regions may require transfinite closure ordinals. The logic dGL, nevertheless, has a sound and complete axiomatization relative to any expressive logic. Separating axioms are identified that distinguish hybrid games from hybrid systems. Finally, dGL is proved to be strictly more expressive than the corresponding logic of hybrid systems.