An Algorithm to Find the Deadlock-Free Conditions on Initial Markings of Resource Places for S3PR

In this paper, an algorithm is proposed to find the conditions on initial markings of resource places ensuring deadlock free for a class of Petri nets, which is called S³PR. This algorithm first finds the strict minimal siphons that can be emptied. Then the conditions ensuring deadlock free for the net are generated. Finally, the minimal sum of tokens in the resource places is computed. In this algorithm, no monitor is added to the net so that structurally complex supervisors are avoided. Furthermore, it gets high resource utilization without exhaustive computation. A simple example is used to illustrate the application of the algorithm.