Affiliations: Université Blaise Pascal (Clermont-Ferrand II), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes, BP 10125, 63173 Aubière Cedex, France. [email protected]; [email protected]
Note: [] Address for correspondence: Université Blaise Pascal (Clermont-Ferrand II), Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes, BP 10125, 63173 Aubière Cedex, France
Note: [] This work was founded by the French National Research Agency, the European Commission (Feder funds) and the Région Auvergne in the Framework of the LabEx IMobS$^3$.
Abstract: The context of this work is the reconstruction of Petri net models for biological systems from experimental data. Such methods aim at generating all network alternatives fitting the given data. To keep the solution set small while guaranteeing its completeness, the idea is to generate only Petri nets being “minimal” in the sense that all other networks fitting the data contain the reconstructed ones. In this paper, we consider Petri nets with extensions in two directions: priority relations among the transitions of a network in order to allow modeling deterministic systems, and control-arcs in order to represent catalytic or inhibitory dependencies. We define a containment relation for Petri nets taking both concepts, priority relations and control-arcs, into account. We discuss the consequences for this kind of Petri nets differing in their sets of control-arcs and priority relations, and the impact of our results towards the reconstruction of such Petri nets.
