An algorithm to find the condition on initial markings of resource places and job places for liveness of S3PMR

In this paper, an algorithm is proposed to find the condition on initial markings of resource places and job places for liveness of S3PMR. The algorithm first finds the strict minimal siphons that can be unmarked. Then, the condition on initial markings is computed under which a strict minimal can't be unmarked. Finally, the condition on initial markings of resource places and job places for liveness of S3PMR is generated. Different from the previous control policies that add monitors to the system, this paper focuses on properly setting the initial markings to get a live model, which avoids the structurally complex supervisors. A simple example is used to illustrate the application of the algorithm.