Keynote talk I: How to prove hybrid systems

Abstract

Hybrid systems combine discrete dynamics with continuous dynamics along differential equations. They arise frequently in many safety-critical application domains, including aviation, automotive, railway, and robotics. But how can we ensure that these systems are guaranteed to meet their design goals, e.g., that an aircraft will not crash into another one? This talk describes how hybrid systems can be proved using differential dynamic logic. Differential dynamic logic (dL) provides compositional logics, programming languages, and reasoning principles for hybrid systems. As implemented in the theorem prover KeYmaera X, dL has been instrumental in verifying many applications, including the Airborne Collision Avoidance System ACAS X, the European Train Control System ETCS, automotive systems, mobile robot navigation, and a surgical robot system for skull-base surgery.