  Our main result is a polynomial time algorithm for deciding realizability for
the GXU sublogic of linear temporal logic. This logic is particularly suitable
for the specification of embedded control systems, and it is more expressive
than GR(1). Reactive control programs for GXU specifications are represented as
Mealy machines, which are extended by the monitoring of input events. Now,
realizability for GXU specifications is shown to be equivalent to solving a
certain subclass of 2QBF satisfiability problems. These logical problems can be
solved in cubic time in the size of GXU specifications. For unrealizable GXU
specifications, stronger environment assumptions are mined from failed
consistency checks based on Padoa's characterization of definability and Craig
interpolation.
