  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.
