Invertibility of Discrete-Event Dynamic Systems

In this paper we consider a class of Discrete-Event Dynamic Systems (DEDS) modeled as finite-state automata in which only some of the transition events are directly observed. An invertible DEDS is one for which it is possible to reconstruct the entire event string from the observation of the output string. The dynamics of invertibility are somewhat complex, as ambiguities in unobservable events are typically resolved only at discrete intervals and, perhaps, with finite delay. A notion of resiliency or error recovery is developed for invertibility, and polynomial-time tests for invertibility and for resilient invertibility, as well as a procedure for the construction of a resilient inverter, are discussed.Research supported by the Air Force Office of Scientific Research under Grant AFOSR-88-0032 and by the Army Research Office under Grant DAAL03-86-K0171. This research was partially done during our stay at the Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Rennes, France, and the second author was also supported by IRISA during this time.