In this paper, we are interested in the discriminability of supervision patterns, in discrete event systems (DES). Discriminability — as opposed to diagnosability — is the possibility to detect the exclusive occurrence of a particular behavior of interest — called the supervision pattern. To this end, we propose to adapt the classical twin-plant approach to Petri nets unfolding. The usage of unfoldings permits us to avoid the combinatorial explosion associated with marking graphs. The method can also be used to solve the classical problem of discrete event systems' diagnosability.