text: 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 @math -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 @math to @math observations from now. We also provide a quadratic algorithm that decides predictability of the system.
  @cite_8: Abstract The problem of predicting the occurrences of a pattern in a partially-observed discrete-event system is studied. The system is modeled by a labeled transition system. The pattern is a set of event sequences modeled by a finite-state automaton. The occurrences of the pattern are predictable if it is possible to infer about any occurrence of the pattern before the pattern is completely executed by the system. A novel off-line algorithm to verify the property of predictability is presented. The verification is polynomial in the number of states of the system. An on-line algorithm to track the execution of the pattern during the operation of the system is also presented. This algorithm is based on the use of a diagnoser automaton.
summary: @PARASPLIT While this is a minor issue, we provide an example and a comprehensive discussion that illustrate the complexity error from J ' @cite_8 . Consider the example of Figure a. This DES includes @math states and @math transitions. The single observable event is @math and the single unobservable event is @math (this example does not feature any faulty event). The twin plant then consists in @math states and @math transitions (details in Table ). The @math -reduction, presented on Figure b, contains one state fewer than the original DES but @math transitions. As a consequence, the number of states in the twin plant reduces down to @math but the number of transitions shoots up to @math (details in Table ).