TITLE:
Petri Nets Representation Approach through Euler Graph
AUTHORS:
Hilaire Nkunzimana, Emile Niyongabo, Egide Ndayizeye, Elie Mushengezi Zihindula, Jérémie Ndikumagenge
KEYWORDS:
Petri Nets, Euler Graphs, Depth-First and Breadth-First Traversal Search, Iterative Algorithm
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.5,
May
30,
2025
ABSTRACT: For decades, engineers have utilized Petri nets to develop automated systems with specific functional requirements or characteristics. Nonetheless, the existing formalism prevents the use of classic traversal techniques to examine and analyze a system’s functional behavior. This paper provides a novel technique to represent Petri nets as directed Euler graphs. It enables design engineers to examine and traverse the various states of a system utilizing the various methodologies and traversal processes applicable to Euler graphs. In this study, we present an iterative approach for determining an optimal path in terms of the least number of edges (vertices) required to cover and contain the system’s states, which are represented as Petri nets. The goal is to leave one vertex and return to the same vertex of the graph in a finite number of steps. This is a new method for determining the attribute of the system’s reset, which is represented by Petri nets and allows the system to return to its starting state, the resting state. The goal is to broaden the ontological basis of Petri nets by displaying linkages or relationships between Petri nets that are akin to directed Euler graphs.