Computation of Minimal Siphons for a Class of Generalized Petri Nets

Siphons are well suited to analyze and control deadlocks in Petri Nets (PN). A formal specification is presented to enable us to exert control to prevent the occurrence of deadlock problems. The approach adopted is Simple Sequential Processes with Resourses SSPR and drives us to distinguish deadlock states with insufficiently marked siphons. Depending on siphon control, a class of Petri nets is applied to calculate minimal siphons with high modelled power and can be modelled to become a focus of the resource circuits of the system. Deadlock prevention is achieved through the utilization of a method proposed to make elementary siphons maximally controlled by adding Control Places (CPs). The simulation PN toolbox is used with MATLAB as a tool to find minimal siphons and simulate the multipurpose manufacturing resources problem to illustrate the reachability graph of a deadlock system. For this purpose, the application system net is used in the analysis and control of the siphons. Finally, two examples are presented to demonstrate how the method works with siphons effect.