O-Minimal Hybrid Systems

A uni ed approach to decidability questions for veri cation algorithms of hybrid systems is obtained by the construction of a bisimulation. Bisimulations are nite state quotients whose reachability properties are equivalent to those of the original in nite state hybrid system. In this paper, we introduce the notion of o-minimal hybrid systems, which are initialized hybrid systems whose relevant sets and ows are de nable in an o-minimal structure. We prove that o-minimal hybrid systems always admit nite bisimulations. We then present a list of o-minimal structures which captures most hybrid systems known to admit nite bisimulations as well as present new classes of hybrid systems with more complex dynamics for which nite bisimulations exist.