AN ANALYTICAL METHOD FOR WELL-FORMED WORKFLOW/PETRI NETS VERIFICATION: CLASSICAL SOUNDNESS

Abstract

In this paper we consider workflow nets as dynamical systems governed by ordinary difference equations described by a particular class of Petri nets. Workflow nets are formal model of business processes. Well-formed business processes correspond to sound workflow nets. Even if it seems considered necessary to require soundness of workflow nets, there exist business processes with conditional behavior that will not necessarily satisfy the soundness property. In this sense, we propose an analytical method for showing that a workflow net satisfies the classical soundness property using a Petri net. To show our statement we use the Lyapunov stability theory to tackle the classical soundness verification problem for a class of dynamical systems described by Petri nets. This class of Petri nets allows a dynamical model representation that can be expressed in terms of difference equations. As a result, applying Lyapunov theory the classical soundness property for workflow nets is solved showing that the Petri net representation is stable. We show that a finite and nonblocking workflow net satisfies the sound property if and only if its corresponding PN is stable, i.e., given the incidence matrix A of the corresponding PN there exists a strictly positive m vector such that A 0: The key contribution of the paper is the analytical method itself that satisfies part of the definition of the classical soundness requirements. The method is for practical applications, guarantees that anomalies can be detected without domain knowledge and can be easily implemented into existing commercial systems that do not support the verification of workflows. Validity of the proposed method is successfully demonstrated by application examples.