Elements of general net theory

Abstract

Some of the main features of a theory of systems in which the concept of concurrency plays a central role are presented. This theory is founded upon a systems model called condition/event-systems (CE-systems). In order to enrich the language concerning CE-systems, three types of completions are carried out. Completion w.r.t. information flow enables us to explicate conflict resolution and brings the notion of information into the theory. T-completion and S-completion lead to a systematic classification of all system invariants, the enloqic structure and the synchronic structure of CE-systems. The relationship between logic and net theory obtained through the enlogic structure is further exploited in a number of different ways. Similarly, the concept of synchronic distance is generalized and applied more directly to the study of systems. From the point of view of applications, it is important to develop a family of net based models. Two such models are exhibited, bipolar synchronization systems and predicate/transiton-nets. The question as to what is meant by a family of net based models is is studied by presenting the category of nets.