Abstract: Lazy computation is not new in model-based diagnosis of active systems (and of discreteevent systems in general). Up to a decade ago, diagnosis methods for discrete-event systems required the (off-line) explicit generation of the system model in order to perform (on-line) diagnosis. Since this systematic approach is impractical when the system is large and distributed, a lazy approach was taken later, which does not require the previous generation of the system model. However, a similar drawback still exists when diagnosis involves an uncertain temporal observation, typically represented by a directed acyclic graph. In order to reconstruct the system behavior based on such an observation, an index space is generated as the determinization of a nondeterministic automaton derived from the observation, the prefix space. The point is that the prefix space and the index space sadly suffer from the same computational difficulties as the system model, with the aggravating that they ...