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. Key words, Automata, Invertibility, Observabitity, Resiliency, Error recovery, Discrete-event dynamic systems.