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. W e 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 an d formulate requirements for the time flow. We show how to compose timed sy stems 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 d evelopment process can be captured as classical refinement steps. (C) 2001 Elsevier Science B.V. All rights reserved.