Information rich enough sample paths for machine identification

Machine identification of discrete event dynamic systems is to reconstruct machine models by a finite length sample path from an unknown machine target. Previous study of online modeling refinement shows that, with increased sample path in length, the reconstructed machines approach the unknown machine in the sense of language equivalence. However, it is not guaranteed that continuingly increased sample path always results in the exact machine reconstruction. In this study, we show that when the unknown target is persistently identifiable, there always exists an information rich enough sample path that uniquely defines the identification target. With the previously reported minimal valid automata algorithm that derives the minimal realization of unknown target, the information rich enough sample path serves as an equivalent representation of the given machine.