  In discrete-event system control, the worst-case time complexity for
computing a system's observer is exponential in the number of that system's
states. This results in practical difficulties since some problems require
calculating multiple observers for a changing system, e.g., synthesizing an
opacity-enforcing supervisor. Although calculating these observers in an
iterative manner allows us to synthesize an opacity-enforcing supervisor and
although methods have been proposed to reduce the computational demands, room
exists for a practical and intuitive solution. Here we extend the subautomaton
relationship to the notion of a subobserver and demonstrate its use in reducing
the computations required for iterated observer calculations. We then
demonstrate the subobserver relationship's power by simplifying
state-of-the-art synthesis approaches for opacity-enforcing supervisors under
realistic assumptions.
