Some Behavioural Aspects of Net Theory

Net theory was initiated by C.A. Petri in the early 60s [29]. The subject matter of tne theory is distributed systems and processes. The key aspect of net theory is that the three fundamental relationships that can exist between the occurrences of a pair of actions at a state are clearly separated from each other at all levels of the theory. These three relationships are (i) at the state s, the action az can occur only after the action a, has occurred (causality); (ii) a, can occur or a2 can occur at s but not both (conflict, choice, indeterminacy); (iii) at the state s both a, and az can occur but with no order over their occurrences (concurrency). Another important feature of net theory is that states and changes-of-states (called transitions) are viewed as two intertwined but distinct entities; they are treated on an “equal” footing by the theory. Over the years net theory has evolved along many directions. It is difficult to give an overview of the whole theory in one place. Hence we shall attempt to do something more modest here. We shall first convey the basic concerns of net theory by presenting a simple system model called elementary net systems. Then we shall give a brief sketch of some of the tools that have been proposed to describe the behuuiour of elementary net systems. We shall concentrate on those tools that have either directly come out of net theory or which have been prodded into existence by the insistence of net theory that causality, conflict and concurrency should be clearly separated from each other in behavioural descriptions of distributed systems. In our presentation we will concentrate on motivations and basic definitions at the expense of stating theorems. The fe-v results that we present are stated without proofs. The proofs can be found in [26]. We shall however leave a trail of pointers to the literature, using which the interested reader can get a reasonable overview of net theory and related topics. In the next section the elementary net system model is presented. Using this model we then define the basic concepts of net theory. This sets the stage for developing the behavioural tools that can capture the essential features of distributed systems