Improved sufficient condition for the controllability of dependent siphons in system of simple sequential processes with resources

Ezpeleta et al. defined a class of Petri nets called system of simple sequential processes with resources, S³PR for short, which can well model some flexible manufacturing systems (FMSs) and present a deadlock prevention policy based on strict minimal siphons (SMS). However, the number of SMS grows exponentially with net size, thereby making the liveness-enforcing supervisor very complex. Li and Zhou proposed an improved policy that allows one to design a much simpler supervisor. They partitioned SMS into dependent and elementary ones, and control dependent ones by controlling elementary ones only. They give a sufficient condition to decide whether a dependent SMS is controlled by its elementary ones. However, this condition is so loose that in most cases the controllability of a dependent SMS cannot be determined although it is actually controlled. The authors propose an improved condition based on a more detailed relationship between dependent and elementary SMS. Finally, an FMS example is used to illustrate the advantage of the proposed condition.