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Consider a two-player game as a bipartite graph G = (S1 U S2, q0, k) with:
two finite set of nodes S1 and S2 with S1 ∩ S2 = ∅; Si, i = 1, 2 is the set of nodes owned by player i,
q0 ∈ S1 is the initial node of the game
k ⊆ (S1 x S1) U (S1 x S2) U (S2 x S1) U (S2 x S1)
A reachability game (G, ...