Duality in high level petri-nets - a basis to do diagnoses

In this paper the relation of high-level Petri-nets (hlpn) and linear algebra is outlined. On the basis of this relation the theory of the dual spaces can be brought in to a new class of hlpn. In this class not only transitions but also places can be marked and each arc is labeled with two mappings, in addition besides transitions also places are firable. By means of an example it is shown that the modified firing rule leads to a behaviour that can be brought in to do diagnoses in hlpn.