Parameterized Net Classes: A Uniform Approach to Petri Net Classes

The concept of parameterized net classes is introduced in order to allow a uniform approach to different kinds of Petri net classes. By different actualizations of the net structure parameter and the data type formalism parameter we obtain several well-known net classes, like elementary nets, place-transition nets, colored nets, predicate transition nets, and algebraic high-level nets, as well as several interesting new classes of low- and high-level nets. First the concept of parameterized net classes is defined on a purely set theoretical level, subsequently we give the concepts taking into account also morphisms and universal properties in the sense of category theory. We explain the underlying notions in an intuitive way. Moreover we give extracts from two of our case studies, where the application of these notions are illustrated in specific net classes, i.e. in instantiations of the parameterized net class.The formal foundation of parameterized net classes this the uniform theory of abstract Petri nets. Low-level abstract Petri nets are a special case of high-level abstract Petri nets, but for better understanding they are presented separately. The theory of abstract Petri nets yields sufficient concepts and results for a specification technique of parameterized net classes. Operational behavior of nets is so presented in a uniform way. Different notions of horizontal structuring, rule-based refinement and their compatibility become available. The horizontal structuring techniques comprise union and fusion of nets. Last but not least we present some examples from our case studies using the notions and results introduced in this paper.