  One of the most interesting questions concerning hierarchical control of
discrete-event systems with partial observations is a condition under which the
language observability is preserved between the original and the abstracted
plant. Recently, we have characterized two such sufficient
conditions---observation consistency and local observation consistency. In this
paper, we prove that the condition of observation consistency is undecidable
for non-regular (linear, deterministic context-free) languages. The question
whether the condition is decidable for regular languages is open.

Systems and Control;Formal Languages and Automata Theory