Structure theory of Petri nets

Abstract

The aim of this tutorial is to give a concise, but nonetheless not too narrow, overview of definitions and results pertaining centrally to Petri net structure theory. The Petri net model considered in these notes are the classical place/transition nets, as they have been defined in the First Advanced Course held in 1979 and originate back to the late Sixties. Structure theory asks what behavioural properties of a Petri net can be derived from its structural properties. Other aspects of Petri nets are neglected to a large extent in the present notes, such as various extensions and generalisations of central notions and results, as well as almost all algorithmic and complexity-theoretic consequences that accompany the structure-theoretic results. Because full proofs can easily be retrieved from the literature, they are not given, unless they are small and perhaps somewhat characteristic for Petri net oriented reasoning. Proof ideas are often sketched, however, and the sharpness of various results is accentuated by means of examples and counterexamples. A list for further reading is also provided. © Springer-Verlag 2013.