Zielonka - Qh

Question

Sept 2022, Problem 5

Can you please explain in game number 1 why Attr1(s0) is {s0,s1,s2,s8}? Can you please explain with the enforcement operator?

Answer 1

attr1({s0}) is the set of states where player 1 can enforce that state s0 is reached, no matter what player 0 will do. Player 1 controls the rectangled states, so all rectangled states that can reach s0 only through rectangled states belong to attr1({s0}). This way, we get s1,s2,s8, but s4 and s6 have to pass through states controlled by player 0, and unfortunately, s3 can always select the transition to s4 so that the states s3,s4,s5,s6,s7 do not belong to attr1({s0}). Hence, attr1({s0}) = {s0,s1,s2,s8}

Comments

is this statement correct in your answer prof?
"attr1({s0}) is the set of states where player 1 can enforce that state s0 is reached, no matter what player 1 will do" or it contains typo?
shall it be: "... no matter what player 0 will do"

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Yes, that is a typo; thanks for pointing out! I have corrected it in the original answer.