Elementary Transition Systems

Transition systems are a simple and powerful formalism for explaining the operational behaviour of models of concurrency. They provide a common framework for investigating the interrelationships between different approaches to the study of distributed systems. Hence an important question to be answered is: which subclass of transition systems corresponds to a particular model of distribted systems? In this paper we provide an answer to this question for elementary net systems. Within net theory, which is one well-established theory of distributed systems, elementary net systems constitute a basic systems model. Using this model, fundamental concepts such as causality, concurrency, conflict and confusion can be clearly defined and separated from each other (see [ 151). Much is known about the behavioural aspects of elementary net systems in terms of trace theory, nonsequential processes and event structures as shown in [lo]. Trace theory was initiated by Mazurkiewicz [7] (see also [l]). The theory of nonsequential processes originates from the work of Petri [12]; see also [2]. Event structures arose out of the work of Nielsen, Plotkin and Winskel [9] and they now possess a rich theory mainly due to the efforts of Winskel [18]. Elementary net systems also have a strong relationship to transition systems. More precisely, there is a natural way of associating a transition system with each elementary net system in order to explain the operational behaviour of elementary net systems in purely sequential terms. Hence the question arises as to which transition systems correspond to elementary net systems.