Understanding the functioning of genetic regulatory networks supposes a modeling of biological processes in order to simulate behaviors and to reason on the model. Unfortunately, the modeling task is confronted to incomplete knowledge about the system. To deal with this problem we propose a methodology that uses the qualitative approach developed by Thomas. A symbolic transition system can represent the set of all possible models in a concise and symbolic way. We introduce a new method based on model-checking techniques and symbolic execution to extract constraints on parameters leading to dynamics coherent with known behaviors. Our method allows us to efficiently respond to two kinds of questions: is there any model coherent with a certain hypothetic behavior? Are there behaviors common to all selected models? The first question is illustrated with the example of the mucus production in Pseudomonas aeruginosa while the second one is illustrated with the example of immunity control in bacteriophage lambda.