What topology tells us about diagnosability in partial order semantics

Abstract

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? When this problem is investigated in the context of 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.