  The Church Problem asks for the construction of a procedure which, given a
logical specification A(I,O) between input omega-strings I and output
omega-strings O, determines whether there exists an operator F that implements
the specification in the sense that A(I, F(I)) holds for all inputs I. Buchi
and Landweber provided a procedure to solve the Church problem for MSO
specifications and operators computable by finite-state automata. We
investigate a generalization of the Church synthesis problem to the continuous
time of the non-negative reals.
  We show that in the continuous time there are phenomena which are very
different from the canonical discrete time domain of the natural numbers.
