A Remark on the Decentralized Diagnosis of Labeled Petri Nets

A remark related to our recent paper is made. Using a counterexample we show that we need more strict assumptions with respect to those used to prove that if a system is diagnosable in a decentralized setting, then it is also diagnosable in a centralized one. Specifically, we require that the central diagnoser sees all the events that can be seen by all the local diagnosers, and that the central diagnoser can distinguish all observable events that the local diagnosers can distinguish on their own.