Transformation methods for generalized Petri nets and their applications to flexible manufacturing systems

Transformation methods are presented for generalized Petri nets by introducing and using the concept of a live and bounded circuit (LB-circuit). An LB-circuit is a generalized version of a simple elementary circuit. The authors also introduce the concept of an arc ratio, which is defined by the arcs´ relations in an LB-circuit and is closely related to the liveness and boundedness of the net. The overlapping relation between two directed paths has an effect on the loss or increase of tokens in the net. Three transformation theorems are given for synthesis and reduction using these concepts. These theorems are used for reducing or synthesizing generalized Petri nets while preserving the liveness and boundedness of the net. The methods consider the dynamic behavior and structure of the net at the same time. The synthesis methods are illustrated for the design of a simple FMS (an assembly process with three robots and two workstations)