Modular transformation methods for generalized Petri nets and their application to automated manufacturing systems

The authors present transformation methods for generalized Petri nets by introducing and using the concept of a live and bounded circuit (LB-circuit), based on fusing common paths. An LB-circuit is a generalized version of a simple elementary circuit. The authors briefly review generalized Petri nets, including their formal definitions and properties, and define an arc ratio, a remainder, and an LB-circuit. A partially overlapping relation is introduced. Using these concepts, four lemmas and three theorems which are the theoretical background for the transformation methods are presented. Reduction methods are described with examples. Synthesis methods are illustrated for a simple automated manufacturing system, a machining/assembly process with three robots and two workstations