Abstract: In this talk we examine the problem of identifying a Petri net system, given a finite language that it generates. First we consider the problem of identifying a free labeled Petri net system, namely all transition labels are distinct. The set of transitions and the number of places is assumed to be known, while the net structure and the initial marking are computed solving an integer programming problem. Then we show how this approach can be extended in several ways introducing additional information about the model (structural constraints, conservative components, stationary sequences) or about its initial marking. Finally, we show how the approach can also be generalized to the case of labeled Petri nets, where two or more transitions may share the same label. In particular, in this case we impose that the resulting net system is deterministic. In both cases the identification problem can still be solved via an integer programming problem.