Structure theory of Petri nets focuses on finding relationships between the behavior of a marked net and the structure of the underlying unmarked net. This approach is particularly interesting as it allows for the analysis of structural properties of Petri nets that depend only on their topological structure, independent of the initial marking.  

These properties can be analyzed using graph theory and algebraic techniques, avoiding exhaustive exploration of the state space, which can generally be computationally expensive or even infinite.  

Algebraic analysis methods, based on the incidence matrix and the associated equations or homogeneous inequalities, enable structural properties (such boundedness, conservativeness, repetitiveness) to be analyzed efficiently but where only the action (firing) part of token game (event) is considered.  

Since these methods completely ignore the crucial condition (enabling) part of the token game, they cannot provide information about complex behavioral properties such as progress and liveness properties, which are fundamental to ensuring the correct, efficient and reliable operation of systems modelled in terms of Petri nets. 

In this talk, we propose to show how approaches based on graph theory improve the applicability and efficiency of algebraic methods. We will highlight their ability to tackle with structural liveness property, to specify the conditions under which this property is monotonic or non-monotonic, and to verify large-scale and complex systems via the development of modular analysis (i.e. by composition or decomposition of Petri nets). 

Kamel Barkaoui is full professor (Exceptional Class) at the Department of Computer Science of Conservatoire National des Arts et Métiers (Le Cnam Paris). He obtained his Ph.D. in Computer Science (1988) and Habilitation à Diriger des Recherches (1998) from Université Paris 6 (Sorbonne University). 

His area of research focuses on formal methods for specifying, verifying, monitoring and evaluating concurrent discrete event systems and also includes discrete mathematics, stochastic modelling and deep reinforcement learning.

Kamel Barkaoui has been visiting professor or invited researcher in the following universities: Polytechnique Montréal (Canada), Xidian University (China), Tshwane University of Technology (South Africa), Tecnologico de Monterrey (Mexico), King Saud University (Saudi Arabia), New Jersey Institute of Technology (USA), Macau University of Science and Technology (Macau), University of Pisa (Italy) , University of Zaragoza (Spain) and in Maghrebian Universities.

He supervised more than 36 PhD theses; he published 55 papers in International Journals and more than 150 peer-reviewed papers in international conferences and contributed to several books. He led or participated in more than 10 international research projects. He received the Outstanding Paper Award at the IEEE Int. Conf. on System Man and Cybernetics (IEEE SMC 1995) and is recipient of the Prime d’Excellence Scientifique du MESRI since 1998.

Kamel Barkaoui served on PCs and as PC chair and OC chair of several international workshops and conferences in his areas of research. He was Program Committee chair of the 3rd International Colloquium on Theoretical Aspects of Computing (ICTAC 2006), General chair of the 18th International Symposium on Formal Methods (FM 2012), General chair of the 35th International Conference on Application and Theory of Petri Nets and Concurrency (Petri Nets 2014) and of the 14th International Conference on Application of Concurrency to System Design (ACSD 2014). 

In 2007, he founded the International Conference on Verification and Evaluation of Computer and Communication Systems (VECoS, 17th edition held in October 2024). More recently, he was Program Committee chair of the 13th Symposium on Reactive Systems Modeling (MSR 2021), Chairman of the Scientific Committee of the 6th CRI 2023 Computer Research Conference and Chairman of the Technical Program Committee of the 17th African Conference for the Research in Computer Science and Applied Mathematics (CARI 2024). 

He was a Guest Editor for Formal Aspects of Computing Journal (FACJ), Journal of Systems and Software (JSS), ACM Transactions on Embedded Computing Systems (TECS), Innovations in Systems and Software Engineering - A NASA Journal (ISSE), Journal of Discrete Event Systems (DEDS) and referee for several prestigious international Journals on Computer Science and on Automatic Control.

Kamel Barkaoui is currently Associate Editor for the International Journal of Critical Computer-Based Systems (IJCCBS) and Editorial Board Member for ARIMA Journal and Current Chinese Science Journal. He was elected member of the Tunisian Academy of Sciences, Letters and Arts (Beït al Hikma) in 2015 and vice-president of the African Society of Digital Sciences (ASDS) in 2022.