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Isn't it satisfy S1 formula and not satisfy S2? 

in * TF "Emb. Sys. and Rob." by (220 points)

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In your transition system, there is only one path that alternates infinitely often between the states labeled with {} and {p,q}. On this path, both formulas S1 and S2 are satisfied, since we have there infinitely often p&q, infinitely often p, and infinitely often q.
by (166k points)
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