Qualitative formalisms offer a well-established alternative to the more tradi-tionally used differential equation models of Biological Regulatory Networks (BRNs). These formalisms led to numerous theoretical works and practical tools to understand emerging behaviors. The analysis of the dynamics of very large models is however a rather hard problem, which led us to previously in-troduce the Process Hitting framework (PH), which is a particular class of non-deterministic asynchronous automata network (or safe Petri nets). Its major advantage lies in the efficiency of several static analyses recently designed to assess dynamical properties, making it possible to tackle very large models. In this paper, we address the formal identification of qualitative models of BRNs from PH models. First, the inference of the Interaction Graph from a PH model summarizes the signed influences between the components that are effective for the dynamics. Second, we provide the inference of all René-Thomas models of BRNs that are compatible with a given PH. As the PH allows the specification of nondeterministic interactions between components, our inference emphasizes the ability of PH to deal with large BRNs with incomplete knowledge on interactions, where Thomas's approach fails because of the combinatorics of parameters. The inference of corresponding Thomas models is implemented using An-swer Set Programming, which allows in particular an efficient enumeration of (possibly numerous) compatible parametrizations.