Computation of Projections for the Abstraction-based Diagnosability Verification

The verification of language-diagnosability (LD) for discrete event systems (DES) generally requires the explicit evaluation of the overall system model which is infeasible for practical systems. In order to circumvent this problem, our previous work proposes the abstraction-based LD verification using natural projections that fulfill the loop-preserving observer (LPO) property. In this paper, we develop algorithms for the verification and computation of such natural projections. We first present a polynomial-time algorithm that allows to test if a given natural projection is a loop-preserving observer. Then, we show that, in case the LPO property is violated, finding a minimal extension of the projection alphabet such that the LPO condition holds is NP-hard. Finally, we adapt a polynomial-time heuristic algorithm by Feng and Wonham for the efficient computation of loop-preserving observers.