  Abstractions of dynamical systems enable their verification and the design of
feedback controllers using simpler, usually discrete, models. In this paper, we
propose a data-driven abstraction mechanism based on a novel metric between
Markov models. Our approach is based purely on observing output labels of the
underlying dynamics, thus opening the road for a fully data-driven approach to
construct abstractions. Another feature of the proposed approach is the use of
memory to better represent the dynamics in a given region of the state space.
We show through numerical examples the usefulness of the proposed methodology.
