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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<strong>Büchi</strong> games<br />
We have shown that Player 0 has a (memoryless) winning strategy<br />
from every state in Attr 0 (Recur 0 (F)), so Attr 0 (Recur 0 (F)) ⊆ W 0 .<br />
And, Player 1 has a (memoryless) winning strategy from every state<br />
in S \Attr 0 (Recur 0 (F)), so S \Attr 0 (Recur 0 (F)) ⊆ W 1 . This implies<br />
the following theorem.<br />
Theorem<br />
Given a <strong>Büchi</strong> game ((S,S 0 ,E),F), the winning regions W 0 <strong>and</strong> W 1<br />
are computable <strong>and</strong> form a partition, i.e., W 0 ∪W 1 = S. Both players<br />
have memoryless winning strategies.<br />
How expensive it the computation of W 0 <strong>and</strong> W 1 ?
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