Comments on "An iterative synthesis approach to petri net based deadlock prevention policy for flexible manufacturing systems"

In the above paper, it proposes a deadlock prevention policy for a flexible manufacturing system (FMS), which needs the complete state enumeration of the FMS that is modeled with Petri nets. The reachability graph of a Petri-net model is divided into two parts: the live zone (LZ) and the deadlock zone (DZ). The states in the LZ of the reachability graph of a Petri net constitute the legal behavior of the net from the viewpoint of deadlock prevention. The concept of first-met bad markings is proposed. A first-met bad marking is a node in DZ, whose father nodes are in LZ. The deadlock prevention policy is used in an iterative way. At each iteration, a first-met bad marking is identified from the reachability graph of a Petri net to be controlled. The reachability of a first-met bad marking is prohibited by adding a monitor, establishing a marking invariance relationship between the additional monitor and the activity places that are marked under the first-met bad marking. To achieve this, without a formal proof, [Lemma 1] is developed as shown in this article.