Polynomial test for Stochastic Diagnosability of discrete event systems

Two types of diagnosability of stochastic discrete-event systems (DESs) were introduced by Thorsley et al. in 2005, where a necessary and sufficient condition for Strong Stochastic Diagnosability (referred as A-diagnosability in [2]), and a sufficient condition for Stochastic Diagnosability (referred as AA-diagnosability in [2]), both with exponential complexity, were reported. In this paper, we present polynomial complexity tests for checking (i) necessity and sufficiency of Strong Stochastic Diagnosability, (ii) sufficiency of Stochastic Diagnosability for arbitrary DESs, and (iii) necessity as well as sufficiency of Stochastic Diagnosability for a class of DESs that have certain ergodicity property. Thus the work presented improves the accuracy as well as complexity of testing stochastic diagnosability.