What Topology tells us about Diagnosability in partial order semantics

From a partial observation of the behaviour of a labeled Discrete Event System, fault Diagnosis strives to determine whether or not a given “invisible” fault event has occurred. The diagnosability problem can be stated as follows: does the labeling allow for an outside observer to determine the occurrence of the fault, no later than a bounded number of events after that unobservable occurrence ? In concurrent systems, partial order semantics adds to the difficulty of the problem, but also provides a richer and more complex picture of observation and diagnosis. In particular, it is crucial to clarify the intuitive notion of “time after fault occurrence“. To this end, we will use a unifying metric framework for event structures, providing a general topological description of diagnosability in both sequential and nonsequential semantics for Petri nets.