Interval Predictability in Discrete Event Systems

In this paper we study the problem of predictability in partially observable discrete event systems, i.e., the question whether an observer can predict the occurrence of a fault. We extend the definition of predictability to consider the time interval where the fault will occur: the $(i,j)$-predictability does not only specify that the fault will be predicted before it occurs, but also that the predictor will be able to predict that its occurrence will occur in $i$ to $j$ observations from now. We also provide a quadratic algorithm that decides predictability of the system.