Classical workflow nets and workflow nets with reset arcs: using Lyapunov stability for soundness verification

This paper presents a novel analytical method for soundness verification of workflow nets and reset workflow nets, using the well-known stability results of Lyapunov for Petri nets. We also prove that the soundness property is decidable for workflow nets and reset workflow nets. In addition, we provide evidence of several outcomes related with properties such as boundedness, liveness, reversibility and blocking using stability. Our approach is validated theoretically and by a numerical example related to traffic signal-control synchronisation.