On the eventual invertibility of discrete event systems and its applications

Considers a discrete event system (DES) modeled by a generalized semi-Markov scheme. The authors view the system as an input-output system, where the input is a sequence of event lifetimes, and the output is the resulting sequence of events, states, and transition epochs. The system is observed via an observation map. In a previous paper (1993), the authors investigated the problem of extracting the event lifetimes from observations of the output without delay, referred to as inversion. In this paper, the authors consider the problem of extracting event lifetimes associated with the output up to a finite time in the past, referred to as eventual inversion. The authors give a general set of necessary and sufficient conditions for eventual invertibility of the system. For an eventually invertible system, the authors give an algorithm to invert the observations to get the event lifetimes. As an application, they describe a method of constructing sample paths of alternative DESs using the extracted event lifetimes by the inversion process