A topological perspective on diagnosis

We propose a topological perspective on the diagnosis problem for discrete-event systems. In an infinitary framework, we argue that the construction of a centralized diagnoser is conditioned by two fundamental properties: saturation and openness. We show that these properties are decidable for omega-regular languages. Usually, openness is guaranteed implicitly in practical settings. In contrast to this, we prove that the saturation problem is PSPACE-complete, which is relevant for the overall complexity of diagnosis.