A computable and compositional semantics for hybrid systems

Hybrid Systems are systems having a mixed discrete and continuous behaviour that cannot be characterised faithfully using either discrete or continuous models only. Due to the intrinsic complexity of hybrid systems, it is highly desirable to describe them compositionally, where large systems are seen as the composition of several simpler subparts that are studied independently. Furthermore, since several problems, including reachability, are undecidable for hybrid systems, the availability of approximate decision procedures is another important feature. In this paper, we propose a purely behavioural formalism for hybrid systems that is compositional and supports approximate decision procedures. The formalism is abstract and sufficiently general to subsume or be a semantic framework for most of the concrete formalisms or languages proposed in the literature.