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--- lat:homework [2009/11/27 22:51]
barbara.jobstmann
+++ lat:homework [2009/11/27 22:51]
barbara.jobstmann
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 ===== 06.11.2009 =====
      - Given a reachability game (G,F), give an algorithm that computes the 0-Attractor(F) set in time O(|E|).
-     - Consider the game graph shown in below and the following winning conditions: a) Occ(ρ) ∩ {1} ≠ ∅ and b) Occ(ρ) ⊆ {1,2,3,4,5,6} and c) Inf(ρ) ∩ {4,5} ≠ ∅. Compute the winning regions and corresponding winning strategies showing the intermediate steps (i.e., the Attractor and Recurrence sets) of the computation.
+     - Consider the game graph shown in below and the following winning conditions: a) Occ(ρ) ∩ {1} ≠ ∅ and b) Occ(ρ) ⊆ {1,2,3,4,5,6} and c) Inf(ρ) ∩ {4,5} ≠ ∅. Compute the winning regions and corresponding winning strategies showing the intermediate steps (i.e., the Attractor and Recurrence sets) of the computation.\\ {{hw1.gif|Figure 1}}
      - Given a game graph G=(S,S<sub>0</sub>,T) and a set F ⊆ S. Let W<sub>0</sub> and W_1 be the winning regions of Player 0 and Player 1, respectively, in the Buchi game (G,F).  Prove or disprove:
        - The winning set of Player 0 in the safety game for (G,W<sub>0</sub>) is W<sub>0</sub>,
@@ Line 16: / Line 16: @@
        - the winning set of Player 1 in the guaranty game for (G,W_1) is W_1, and
        - if f_1 is a winning strategy for Player 1 in the guaranty game for (G,W<sub>0</sub>), then f_1 is a winning strategy in the Buchi game (G,F).
-{{hw1.gif|Figure 1}}
 ===== 13.11.2009 =====