Predictability of discrete event systems

The author formulates the trajectory prediction problem by using automaton and language theory. He shows that the automaton method and the perturbation analysis method, which have been developed independently and so far appear to have little relation to each other, can support each other: the former can be used to formulate formally the concept of the latter, and the latter provides an application area for the former. The author defines the predictability of the trajectories of a DES (discrete-event system) based on the trajectories of another DES. The predictability is explained by the projection of a language onto another language. Examples are given to show the application of this concept. It is concluded that the concept introduced here can be viewed as an extension of the controllability and observability theory of DES as well as a generalization of the perturbation analysis theory.