  This paper demonstrates an equivalence between observation problems, control
problems (with partial observation), and diagnosis problems of decentralized
discrete-event systems, namely, the three classes of problems are Turing
equivalent, as one class Turing reduces to another.
  The equivalence allows decomposition of a control problem into a collection
of simpler control sub\-/problems, which are each equivalent to an observation
problem; and similarly allows converting a diagnosis problem to a formally
simpler observation problem. Since observation problems in their most general
formulation have been shown to be undecidable in previous work, the equivalence
produced here demonstrates that control problems are also undecidable; whereas
the undecidability of diagnosis problems is a known result.
