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I'm not getting how to solve the below problem, can you please help with the logic

in * TF "Intelligent Systems" by (280 points)

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Well, that is simply something that you need to learn (and to remember). On slide 44 of the omega-automata chapter, the boolean operations on  omega-automata are described, slides 50 and 51 describe how boolean operations on the acceptance conditions can be performed (if at all), and slides 60 and 61 discuss which automata can be expressed in terms of weaker ones.

On slide 60, you find the formula that is used in the solution to express Fb as a deterministic FG-automaton.

Maybe these slides are a recommendation for a cheat sheet.
by (166k points)
Thank you so much. I got it.
Whcih formula should we use if expression is given as "a strong until b"? Like in 2021 paper, problem 5a,b?
Well, there are many possible solutions (seeω-automata-feb-2021). If you have doubts, simply use the standard translation from LTL to omega-automata, and think about how to (possibly) simplify the acceptance condition.

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