  Conditions preserving observability of specifications between the plant and
its abstraction are essential for hierarchical supervisory control of
discrete-event systems under partial observation. Observation consistency and
local observation consistency were identified as such conditions. To preserve
normality, only observation consistency is required. Although observation
consistency preserves normality between the levels for normal specifications,
for specifications that are not normal, observation consistency is insufficient
to guarantee that the supremal normal sublanguage computed on the low level and
on the high level coincide. We define modified observation consistency, under
which the supremal normal sublanguages of different levels coincide. We show
that the verification of (modified) observation consistency is PSPACE-hard for
finite automata and undecidable for slightly more expressive models than finite
automata. Decidability of (modified) observation consistency is an open
problem. Hence we further discuss two stronger conditions that are easy to
verify. Finally, we illustrate the conditions on an example of a railroad
controller and on a case study of a part of an MRI scanner.
