On the Computation of Natural Observers in Discrete-Event Systems

We continue the work of Wong and Wonham on discrete-event observers, by specializing their algorithms for general causal reporter maps to natural projections. Unlike the former, a natural projection does not always admit a unique smallest extension to a natural observer. Instead there may exist several minimal extensions to the original observable event set. We show that the problem of finding such a minimal extension is NP-hard. However, we propose a polynomial-time algorithm that always finds some extension to a natural observer. While this is not guaranteed to be minimal, it is in practice often reasonably small