On Minimality and Equivalence of Petri Nets

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 tting 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 tting 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 the modelization of deterministic systems, and control-arcs in order to represent catalytic or inhibitory dependencies. We de ne a containment relation for Petri nets taking both concepts, priority relations and controlarcs, into account. We discuss the consequences for extended Petri nets di ering in their sets of control-arcs and priority relations, and the impact of our results towards the reconstruction of such Petri nets.