An analytical method for well-formed workflow/Petri net verification of 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 a formal model of business processes. Well-formed business processes correspond to sound workflow nets. Even if it seems necessary to require the 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 present our statement, we use 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, by applying Lyapunov theory, the classical soundness property for workflow nets is solved proving that the Petri net representation is stable. We show that a finite and non-blocking 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 Φ strictly positive m vector such that AΦ ≤ 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 designed 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. The validity of the proposed method is successfully demonstrated by application examples.

Improving Synchronous Dataflow Analysis Supported by Petri Net Mappings

“…They are a graphical and mathematical modeling tool. In the past few decades, several special classes have been developed to support specific application fields (such as workflows [21] or for developing a decision process [22]), which culminated in some cases in the development of several software tools, such as TINA (TIme petri Net Analyzer) [23], SESA [24], GreatSPN (Generalized Stochastic Petri Nets) [25], CPN (Colored Petri Net) Tools [26], and IOPT (Input Output Place Transitions Nets)-Tools [27,28], just to name a few very successful examples from the academic context. To obtain a picture of the multitude of oriented-based Petri net software tools developed so far, please refer to Petri Nets Tools Database Quick Overview (https://www.informatik.uni-hamburg.de/TGI/PetriNets/tools/quick.html).…”

Analysis of safeness in a Petri net-based specification of the control part of cyber-physical systems

“…Modelling a Petri net-based system offers many advantages compared with other modelling techniques. The graphical representation of Petri nets makes the models relatively simple and legible, and well-developed analysis methods such as invariants and reachability easily detect certain anomalies of system behaviours (Ran et al 2018a;2018b;Koh and DiCesare, 1990;Murata, 1989;Clempner, 2014;Ramirez-Trevino et al, 2007;Ran et al, 2017).…”