The modeling of Biological Regulatory Networks (BRNs) relies on background knowledge, deriving either from literature and/or the analysis of biological observations. But with the development of high-throughput data, there is a growing need for methods that automatically generate admissible models. Our research aim is to provide a logical approach to infer BRNs based on given time series data and known influences amoung genes. In this paper, we propose a new methodology for models expressed through a timed extension of the Automata Networks [22] (well suited for biological systems). The main purpose is to have a resulting network as consistent as possible with the observed datasets. The originality of our work consists in the integration of quantitative time delays directly in our learning approach. We show the benefits of such automatic approach on dynamical biological models, the DREAM4 datasets, a popular reverse-engineering challenge, in order to discuss the precision and the computational performances of our algorithm.