Reachability and Büchi Games - Rich Model Toolkit
Reachability and Büchi Games - Rich Model Toolkit
Reachability and Büchi Games - Rich Model Toolkit
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Duality Between Players<br />
Assume we have a partition of the state space S = P 0 ∪P 1 (i.e.,<br />
P 0 ∩P 1 = ∅) <strong>and</strong> we want to prove W 0 = P 0 <strong>and</strong> W 1 = P 1 .<br />
We want to prove P 0 ⊇ W 0 , P 0 ⊆ W 0 , P 1 ⊇ W 1 , <strong>and</strong> P 1 ⊆ W 1 .<br />
Since we know that W 0 ∩W 1 = ∅ holds, it is sufficient to prove<br />
P 0 ⊆ W 0 <strong>and</strong> P 1 ⊆ W 1 .<br />
P 0 ⊆ W 0 P 1 ⊆ W 1<br />
S \P 0 ⊇ S \W 0 S \P 1 ⊇ S \W 1<br />
P 1 ⊇ S \W 0 ⊇ W 1 P 0 ⊇ S \W 1 ⊇ W 0<br />
P 1 ⊇ W 1 P 0 ⊇ W 0
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