Petri net modules in the transformation-based component framework

Component-based software engineering needs to be backed by thorough formal concepts and modeling techniques. This paper combines two concepts introduced independently by the two authors in previous papers. On one hand, the concept of Petri net modules introduced at IDPT 2002 in Padberg J. Padberg, Petri net modules, Journal on Integrated Design and Process Technology 6 (4) (2002) 105–120], and on the other hand a generic component framework for system modeling introduced at FASE 2002 in Ehrig et al. H. Ehrig, F. Orejas, B. Braatz, M. Klein, M. Piirainen, A generic component concept for system modeling, in: Proceedings of FASE ’02, Lecture Notes in Computer Science, vol. 2306, Springer, 2002]. First we develop a categorical formalization of the transformation based approach to components that is based on pushouts. This is the frame in which we show that Petri net modules can be considered as an instantiation of the generic component framework. This allows applying the transformation based semantics and compositionality result of the generic framework to Petri net modules. In addition to general Petri net modules we introduce Petri net modules preserving safety properties which can be considered as another instantiation of pushout based formalization of the generic framework.