Some Behavioural Aspects of Net Theory

Abstract

Net theory was initiated by C.A. Petri in the early 60's. 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 behaviour of elementary net systems.

Section 2 develops some notation and introduces a purely sequential mode of behavioural description called firing sequences. In the next section the theory of traces which have an independent existence is used to recover information concerning concurrency from the firing sequences. In section 4 the notion of non-sequential processes is introduced.

Both trace theory and the theory of non-sequential processes represent concurrency directly but handle information concerning conflict in an indirect fashion. One must work with the whole set of traces or non-sequential processes in order to talk about conflicts and that too in an indirect fashion. This disadvantage can be overcome with the help of behavioural tools called unfoldings and labelled event structures that are presented in section 5.