Marking diagnosability verification in labeled Petri nets

Abstract

This paper studies the marking diagnosability verification problem in labeled Petri nets. Marking diagnosability is a property implying the fact that a plant Petri net has ever reached a pre-defined set of faulty markings can be detected in a finite number of future steps. We first show that the conventional basis-reachability-graph-based methods cannot be used due to the existence of partially faulty basis markings. To overcome such a problem, we propose a transition partition rule to obtain two particular graphs called the positive basis reachability graph and the negative basis reachability graph. Then we develop an information structure, called a dual verifier, that is a parallel composition of the two basis reachability graphs and can be used to determine the marking diagnosability of a plant net. The proposed method has polynomial complexity in the number of basis markings.