Checking system boundedness using ordinary differential equations

Boundedness is one of the most important properties of discrete Petri nets. Determining the boundedness of a Petri net is usually done through building coverability graph or coverability tree. However, the computation is infeasible for complex applications because the size of the coverability graph may increase faster than any primitive recursive functions. This paper proposes a new technique to check the boundedness without causing this problem. Let a concurrent system be represented by a (discrete) Petri net. By relaxing the (discrete) Petri net to a continuous Petri net, we can model the concurrent system by a family of ordinary differential equations. It has been shown that the boundedness of the discrete Petri net is equivalent to the boundedness of the solutions of the corresponding ordinary differential equations. Hence, we can check the boundedness of a (discrete) Petri net by analyzing the solutions of a family of ordinary differential equations. A case study demonstrates the benefits of our technique.