Well, it's not important that we ask for G¬b, the bigger question behind is whether a property G(p) can be expressed by a deterministic FG automaton. Such questions are discussed in a section of the chapter on omega-automata, and that particular question is answered on slide 60. There you simply find the answer and the omega-automaton mentioned here. So, here it is not a algorithm learned, here it is that theorem/formula/example which should be remembered.
