Towards Algebraic High-Level Systems as Weak Adhesive HLR Categories

Adhesive high-level replacement (HLR) systems have been recently established as a suitable categorical framework for double pushout transformations based on weak adhesive HLR categories. Among different types of graphs and graph-like structures, various kinds of Petri nets and algebraic high-level (AHL) nets are interesting instantiations of adhesive HLR systems. AHL nets combine algebraic specifications with Petri nets to allow the modeling of data, data flow and data changes within the net. For the development and analysis of reconfigurable systems, not only AHL schemas based on an algebraic specification and AHL nets using an additional algebra should be considered, but also AHL systems which additionally include markings of nets. In this paper, we summarize the results for different kinds of AHL schemas and nets, and extend these results to AHL systems. The category of markings is introduced, which allows a general construction combining AHL nets with possible markings leading under certain properties to a weak adhesive HLR category.