Functional dependencies (FDs) can be used for various important operations on data, for instance, checking the consistency and the quality of a database (including databases that contain complex data). Consequently, a generic framework that allows mining a sound, complete, non-redundant and yet compact set of FDs is an important tool for many different applications. There are different definitions of such sets of FDs (usually called cover). In this paper, we present the characterization of two different kinds of covers for FDs in terms of pattern structures. The convenience of such a characterization is that it allows an easy implementation of efficient mining algorithms which can later be easily adapted to other kinds of similar dependencies. Finally, we present empirical evidence that the proposed approach can perform better than state-of-the-art FD miner algorithms in large databases.