Hierarchies of place/transition refinements in Petri nets

Place and transition refinements provide a convenient method of structuring complex net models by replacing single elements (places and transitions) at a "higher-level" of abstraction with "lower-level", more detailed, subnets. The concepts of static and dynamic place/transition refinements are introduced. Dynamic refinements do not increase the size of the (refined) model because no "expansion" of the model is performed; instead, only a "logical" association of higher-level elements with lower-level subnets is maintained and used in model analysis. Multiple applications of place/transition refinements results in hierarchical net models. The paper formalizes the concept of hierarchies of refinements in Petri nets and shows simple applications of the hierarchical approach to modeling of manufacturing cells.