Diagnosability of Labeled Petri Nets via Integer Linear Programming

The problem of diagnosability of a fault after the firing of a finite number of observable events (i.e., K-diagnosability) is tackled in this paper. This problem corresponds to diagnosability of a fault within a finite delay in the context of discrete event systems (DESs). Two results for DESs modeled as labeled Petri nets are given: the first is a sufficient condition for K - undiagnosability of fault, while the second is a necessary and sufficient condition for K-diagnosability. The proposed results exploit the mathematical representation of Petri nets and the Integer Linear Programming standard optimization tool.