Formal Relationship between Petri Nets and Graph Grammars as Basis for Animation Views in GenGED

Specification techniques like Petri nets allow for the formal description and analysis of systems. Although tool support exists for many different Petri net classes and tasks, a domain-specific animation of net behavior, however, is not yet supported by many Petri net tools. In this contribution, we present a formal approach for the generic specification of several Petri net classes including animation views. The approach follows the notions of GenGED, a tool for the visual specification of visual languages based on algebraic graph transformation. Moreover, we give a proof of the semantical compatibility of Algebraic High-Level Petri nets and their representation as graph grammars in GenGED. The proof is based on the formal semantics of Petri net behavior and the construction of graph derivations as pushouts in the category of graphs and graph morphisms. Based on the behavior equivalence, we can define animation views for specific Petri nets in GenGED: the animation view of a system modeled as a Petri net consists of a domain-specific layout and animation rules according to the graph grammar representation of the Petri net.