Refinement of time

We discuss mathematical models of the timed behaviour of system components. We study reactive system components that relate input-to-output streams. We work out a hierarchy of timing concepts. We distinguish non-timed streams, discrete streams with discrete or with continuous time, and dense streams with continuous time. We introduce a notion of a timed system component and formulate requirements for the time flow. We show how to compose timed systems in a modular way. We demonstrate that the introduction of time into a system model as well as the change of the timing model during the system development process can be captured as classical refinement steps.