Logical Analysis of Hybrid Systems - A Complete Answer to a Complexity Challenge

Hybrid systems are systems with interacting discrete and continuous dynamics. They are models for understanding, e.g., computer systems interfacing with the physical environment. Hybrid systems have a complete axiomatization in differential dynamic logic relative to continuous systems. They also have a complete axiomatization relative to discrete systems. Moreover, there is a constructive reduction of properties of hybrid systems to corresponding properties of continuous systems or to corresponding properties of discrete systems. We briefly summarize and discuss some of the implications of these results.