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Fault detection is quite important for discrete event systems. We investigate K-codiagnosability of Petri nets in this paper under the framework that some local sites monitor the operation of the system using their own masks. They exchange information with a coordinator while do not communicate with each other. A fault is detected when there exists a site can diagnose it. We recall the notion of Modified Verifier Nets (MVNs), and prove that K-codiagnosability can be verified looking at some special cycles in the reachability or coverability graph of the MVN. In particular, the proposed approach is available for bounded and unbounded nets. Finally, we give an algorithm to compute the minimum value of K .

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