Identification of deterministic Petri nets

In a previous paper we presented an approach to identify a Petri net system, given a finite language that it generates. 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. In this paper we extend this approach in two ways. Firstly, we consider the case in which the number of places of the net is not given but only an upper bound on its value is known. Secondly, we show how the approach can be extended to the case of deterministic 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