Preserving Languages and Properties in Stepwise Refinement-Based Synthesis of Petri Nets

The current stepwise refinement operation of Petri nets mainly concentrates on property preservation, which is an effective way to analyze and verify complex systems. Further steps into this field are needed from the perspective of system synthesis and language preservation. First, the refinement of Petri nets is introduced based on a k-well-behaved Petri net, in which k tokens can be processed. Then, according to the different compositions of subsystems, well-, under- and overmatched refined Petri nets are proposed. In addition, the language and property relationships among sub-, original, and refined nets are studied to demonstrate behavior characteristics and property preservation in a system synthesis process. A manufacturing system is given as an example to illustrate the effectiveness of the proposed approach in synthesizing and analyzing the Petri nets of complex systems.