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 rime, and dense streams with continuous rime. 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. (C) 2001 Elsevier Science B.V. All rights reserved.