Lecture 3

Recall that a model in the context of games with reachability objectives is a marked graph G = ((S,E), (S1, S2)), where S is the finite set of states, E the set of edges and S1 and S2 partition S. We abbreviate n = |S| and m = |E|. For any s in S, let E(s) = {s′ ∈ S | (s, s′) ∈ E} and assume that for all s in S, E(s) 6= ∅. T ⊆ S denotes the set of target states. Intuitively1 player 1 and player 2 play the following game starting at some s in S: Repeatedly player 1 and player 2 perform steps in the following way: if s in S1 (S2), player 1 (2) chooses a successor state from E(s), from where on the next step is started. Player 1 wins the game if she manages to reach some s in T . Conversely, player 2 wins the game if she manages to stay in S \ T forever. In the last lecture it was shown that