Predictability for Finite State Machines: a set-membership approach

In this paper we investigate how to predict the future occurrence of specific discrete states of a finite state system on the basis of the observations. Predictability property is defined with respect to a subset of discrete states, called critical set, representing for example faulty states or, more generally, any subset of states which is of particular interest from the system's behavior point of view. We define and characterize eventual and critical predictability properties by means of a set-membership-based formalism. Using the proposed framework, it is possible to check predictability properties with polynomial time algorithms.