Engineering safe and reliable systems demands rigorous approaches such as formal methods, using models. Since models are not always available, one needs to infer them from software artifacts. This paper defines a new inference approach for input-output systems that is based on FSM-based testing theory. Central to the approach is the notion of initial quotient of an FSM associated with a partial characterization set that controls the precision of this approximated model. The proposed method infers a model of a system under test by building increasingly precise quotients of it using counterexamples. Various experiments demonstrate its practical usability.