Siphon classification for deadlock prevention in Petri nets

In Petri nets modeling and control of flexible manufacturing systems, the occurrence of deadlock states must be avoided with suitable design techniques. Many of these are based on siphon control, i.e. they implement generalized mutual exclusion constraints that avoid the emptying of siphons. If all minimal siphons are controlled, an excessive computational load may be required to complete the control sub-net and the latter may turn out to be over-sized. A classification of minimal siphons that selects a minimal number of siphons for the control design is proposed in this work. The classification can be exploited to obtain minimum size maximally permissive controllers. Some examples are provided to demonstrate the feasibility of the approach.