System behaviour models with discrete and dense time

This paper deals with techniques and methods for modelling systems that work on discrete and also on continuous streams of data. Such systems are called hybrid systems. We model the interface behaviour of such systems by functions that map streams of input onto streams of output data. I/O state machines, also known as Mealy (and as Moore) machines, can model such systems. Their observable behaviour, called interface abstraction, is modelled by functions on sets of discrete and hybrid streams. We work out foundations for specifying and abstracting such systems as well as refinements of continuous streams into discrete ones. By introducing event views as logical abstraction of continuous streams the logical behaviour of continuous systems in terms of discrete events is captured. This provides a concept of logical abstraction for continuous streams in terms of discrete event streams.