Complexity of Detectability, Opacity and A-Diagnosability for Modular Discrete Event Systems

TL;DR

This paper analyzes the computational complexity of determining detectability, opacity, and A-diagnosability in modular discrete event systems, revealing that these problems are generally harder than in monolithic systems, with some cases being PSPACE-complete and others EXPSPACE-complete.

Contribution

It establishes the complexity classifications for these properties in modular systems, extending previous monolithic system results and identifying special cases with lower complexity.

Findings

Deciding modular weak detectability is EXPSPACE-complete.

Deciding these properties is PSPACE-complete when all unobservable events are private.

Fully observable systems have PSPACE-complete detectability and opacity problems.

Abstract

We study the complexity of deciding whether a modular discrete event system is detectable (resp. opaque, A-diagnosable). Detectability arises in the state estimation of discrete event systems, opacity is related to the privacy and security analysis, and A-diagnosability appears in the fault diagnosis of stochastic discrete event systems. Previously, deciding weak detectability (opacity, A-diagnosability) for monolithic systems was shown to be PSPACE-complete. In this paper, we study the complexity of deciding weak detectability (opacity, A-diagnosability) for modular systems. We show that the complexities of these problems are significantly worse than in the monolithic case. Namely, we show that deciding modular weak detectability (opacity, A-diagnosability) is EXPSPACE-complete. We further discuss a special case where all unobservable events are private, and show that in this case the problems are PSPACE-complete. Consequently, if the systems are all fully observable, then deciding weak detectability (opacity) for modular systems is PSPACE-complete.