On the Computation of Natural Observers in Discrete-Event Systems

Abstract

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.

On the Computation of Natural Observers in Discrete-Event Systems

“…To exploit the reduction power of natural observers (Feng 2007;Feng andWonham 2006a, 2008;Hill and Tilbury 2006;Pena et al 2006;, an efficient algorithm is needed to verify and compute them (Feng and Wonham 2006b). Recall that natural projection is a special type of causal reporter, for which Wong and Wonham (2004) have proposed a polynomial-time algorithm on the computation of observers.…”

“…Section 10 states the conclusion. A summary version of this paper has been published in (Feng and Wonham 2006b). …”

Synthesis of controllable and normal sublanguages for discrete-event systems using a coordinator

“…In a typical situation, the projected models are significantly smaller than the original models. The reader is referred to [15,16] for more details.…”

Generalised Verification of the Observer Property in Discrete Event Systems

“…In (Wong and Wonham, 1996), the abstraction is obtained in the form of a reporter map, which projects strings of events of the original (low-level) model, built from a set Σ, into highlevel strings built from an independent set T of events. Due to some difficulties with the use of reporter maps (Feng and Wonham, 2010), most of the approaches subsequent to (Wong and Wonham, 1996) focus on abstractions ob-tained by the natural projection, which maps strings of the original model into strings of the abstraction, by erasing events of Σ which are not contained in a given subset of relevant events Σ r ⊆ Σ, like in (Wong et al, 2000;Cunha and Cury, 2007;Feng and Wonham, 2008;Schmidt and Breindl, 2008).…”

“…The OP-verifier does not require explicitly computing the abstraction to check for the OP and has been shown to have better computational performance when compared to other similar procedures (Wong and Wonham, 2004;Jiang et al, 2003;Feng and Wonham, 2010;Pena et al, 2010a). Nevertheless, the OP-verifier algorithm as proposed in (Pena et al, 2008) can only be applied to automata that do not have cycles of non-relevant events.…”