The Process Hitting (PH) is a recently introduced framework to model concurrent processes. Its major originality lies in a specific restriction on the causality of actions, which makes the formal analysis of very large systems tractable. PH is suitable to model Biological Regulatory Networks (BRNs) with complete or partial knowledge of cooperations between regulators by defining the most permissive dynamics with respect to these constraints. On the other hand, the qualitative modeling of BRNs has been widely addressed using René Thomas' formalism, leading to numerous theoretical work and practical tools to understand emerging behaviors. Given a PH model of a BRN, we first tackle the inference of the underlying Interaction Graph between components. Then the inference of corresponding Thomas' models is provided using Answer Set Programming, which allows notably an efficient enumeration of (possibly numerous) compatible parametrizations. In addition to giving a formal link between different approaches for qualitative BRNs modeling, this work emphasizes the ability of PH to deal with large BRNs with incomplete knowledge on cooperations, where Thomas' approach fails because of the combinatorics of parameters.