program synthesis (reactive synthesis)

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5 Reactive Synthesis: 6 points Solve the following reactive synthesis problem. A depiction of the situation is given in Figure 1. You have to synthesize a controller for a traffic light that has the following inputs, outputs, and requirements. Input signals • C: car is waiting on farm road • P: pedestrians want to cross the highway 2 Figure 1: Road Intersection • Eh: emergency vehicle on highway • Ef: emergency vehicle on farm road Outputs signals • h: highway light is green • f: farm road light is green Requirements • Lights should not be both green • Lights should both turn green every now and then • If pedestrians approach, farm light should go green (i.e. on input, the system should immediately output f). You have to: • Formalize the requirements in LTL; • Is the system realizable? If so provide a controller otherwise provide a winning strategy for the environment.

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