“…For state (5Y, {4Y, 5Y }, {0N, 1N, 2Y, 3Y, 4Y, 5Y }), when event a occurs, it reaches (7Y, {6Y, 7Y, 8N, 9N, 9Y }, {7Y }), where since a ∈ Σ o but 7Y / ∈ Xr , the third component is updated according to the second case of Equation ( 4 Theorem 2 Let Obs( G) be the DIRM-observer for system G. Then system G is current-state opaque w.r.t. X S and X r if and only if ∀x obs ∈ X obs : X 3 (x obs ) XS (13) We illustrate Theorem 2 by the following example. 3), where for x = (7Y, {6Y, 7Y, 8Y, 9Y, 9N }, {7Y }), we have X 3 (x) = {7Y } ⊆ XS .…”