Conducted jointly by Mines Nantes and ECN, this research explores Petri nets for modeling complex systems.
The Essentials: Conducted jointly by Mines Nantes and ECN, this research explores Petri nets for modeling complex systems.
Maurice Comlan, researcher at IRCCyN; LETIA (Mines Nantes).
Thesis defended in 2016 at the doctoral school EDSTIM; LETIA.
This research was carried out under a Franco-Beninese joint supervision (cotutelle), ensuring simultaneous grounding in local field realities and international academic standards.
Context and Research Question
Petri nets are a well-established formalism for modeling discrete-event systems, particularly in the fields of automation and verification. The need for verification and validation in these systems is critical, since minor errors can have serious consequences. Analyzing a system's behavior often requires constructing a state graph that exhaustively enumerates reachable states. However, this construction faces a combinatorial explosion problem, resulting from the complexity and concurrency inherent to the systems being modeled. This phenomenon complicates analysis, making it difficult to guarantee system reliability.
Unfolding is a technique that shows promise for mitigating this problem by focusing on the partial orders between events. This method simplifies analysis while maintaining system verifiability. In particular, unfolding is well suited to Petri nets with reset arcs, where complexity is increased. The study of this technique is a central focus of Maurice Comlan's thesis, which aims to contribute to the analysis of branching processes derived from Petri net unfolding.
Methodology
The research relies on a theoretical approach combined with modeling techniques. The study begins with an in-depth analysis of Petri nets and their extensions. The properties of discrete-event systems are examined, with emphasis on how unfolding can be applied to manage combinatorial explosion. The methodology also includes the development of a specific algebra for branching processes derived from unfolding, allowing exploration of the implications of this approach for system verification and validation.
Experiments and simulations were conducted to evaluate the effectiveness of the unfolding method. These tests explored various application scenarios in complex systems, observing how the unfolding technique can reduce the number of states in the state graph while preserving essential properties such as liveness and deadlock-freedom. This approach validated the hypotheses formulated and refined the available analysis tools.
Key Findings
The results of this research reveal several significant advances in the field of Petri nets. First, the thesis identifies effective methods for reducing combinatorial explosion when constructing state graphs. By applying unfolding, it is possible to retain only the partial orders between events, considerably reducing the number of states to be analyzed.
Second, the development of a specific algebra for branching processes derived from unfolding brings a new dimension to system analysis. This algebra makes it possible to formalize the relationships between different possible executions, offering a better understanding of branching processes compared with classical processes. Experimental results show that this approach improves system verifiability while ensuring compliance with safety and reliability requirements.
Finally, the thesis highlights the importance of international collaboration in Petri net research. The Franco-African joint supervision enriched perspectives and strengthened the tools developed, which could have significant implications for the modeling and analysis of complex systems across various industrial sectors.
Discussion and Outlook
The Petri net unfolding approach developed in this thesis opens new avenues for future research. By simplifying the analysis of discrete-event systems, this method could be extended to other types of complex systems, enabling better complexity management and improved reliability. The implications of the results obtained go beyond purely theoretical modeling; they offer practical tools for sectors where safety is paramount.
Integrating this method into existing systems could also facilitate the transition to more robust and adaptive solutions. Further research could explore applying unfolding in varied contexts, such as the Internet of Things or embedded systems. Moreover, developing software based on the branching-process algebra could prove beneficial for engineers and decision-makers, providing them with effective tools for verification and validation.
Continuing this research within international collaborations could further enrich the field of Petri nets and provide innovative solutions to the challenges encountered in complex system analysis.
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Sources and Access
Maurice Comlan. Contribution au dépliage des réseaux de Petri et à l'analyse des processus de branchement.. Informatique [cs]. Université de Nantes; Université d'Abomey-Calavi, 2016. Français. ⟨NNT : ⟩. ⟨tel-01542989⟩