In: Bulletin of the EATCS, Vol. 66, pages 85-91. October 1998.
Abstract: We have introduced a formal framework for the classification of Petri nets (e.g. Padberg 1997, Abstract Petri Nets: A Uniform Approach and Rule-Based Refinement). This framework describes the net structure using adjoint functors and - in case of high-level nets - the data type part using institutions and specification frames. In this paper we extend this framework. This extension is independent of the description of the data type part. Hence it suffices to consider merely low-level Petri nets like different kinds of place/transition nets, ordinary nets, elementary nets, and so on. Quite many Petri net types the structure of the marking differs from the structure of the flow given by the underlying net structure. Thus we introduce here one description for the flow structure and one for the marking structure. These descriptions are given by two different adjoint functors, relating the underlying sets of transitions and places to the corresponding flow structure and to the corresponding marking structure. We first introduce several net types and discuss their flow and marking structure. Then we describe flow and marking structure in terms of adjoint functors. Subsequently we give the classification of low-level Petri nets according to these adjunctions.
Keywords: Petri nets, classification, category theory.