Abstract
There is a growing need for the top-down design methodology for Discrete Event Systems (DES). Establishing a firm foundation of such methodology is the central topic of this paper. In a top-down design of a discrete event system, one starts with a high-level model of the system and refines it stepwise until a sufficient low-level model has been reached. Therefore, in this paper, we study the following two things to make the top-down design useful: The first is a theory of formal models of DES which are suited to refinement, and the second is an adequate notion of refinement relation between the models. Firstly, in order to get a new DES's model, we extend the state machines, a well-known DES's model, by introducing the ‘composite event’ into the set of events. This enables us to refine an event in a high-level model by composing several events in a low-level model. Then, to get an adequate refinement relation, we firstly define a ‘canonical model’ called Proper-model which has the simplest state space in a set of models that have the same set of events and the same state transitions. The reason to define such a canonical model is that to refine a model effectively, it's always expected to refine the model with as fewer elements as possible. So, we define a refinement relation only between Proper-models. Finally, we show that the refinement relation defined in this paper has the transitive property which is indispensable for stepwise refinement.
