Reachability and Büchi Games - Rich Model Toolkit

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Summary We know how to solve Büchi and Co-Büchi games by positional winning strategies. In LTL, ◮ ✸F = reachability ◮ ✷F = safety ◮ ✷✸F = Büchi ◮ ✸✷F = Co-Büchi
Exercise 2. 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.
Page 1 and 2: Reachability and Büchi Games Barba
Page 3 and 4: Reachability and Safety Games
Page 5 and 6: Force Visit in Next Step Given a se
Page 7 and 8: Computing the Attractor Constructio
Page 9 and 10: Example s 5 s 7 Attr 0 0 = {s 3 ,s
Page 11 and 12: Example s 5 s 6 s 7 Attr 0 0 = {s 3
Page 13 and 14: Example s 5 s 3 s 6 s 4 s 7 Attr 0
Page 15 and 16: Computing the Attractor Constructio
Page 17 and 18: 0-Attractor To show W 0 = Attr 0 (F
Page 19 and 20: 0-Attractor cont. Proof cont. S \At
Page 21 and 22: Summary We know how to solve reacha
Page 23 and 24: Exercise 1. Given a reachability ga
Page 25 and 26: Büchi and co-Büchi Games
Page 27 and 28: Idea Compute for i ≥ 1 the set Re
Page 29 and 30: One-Step Attractor We count revisit
Page 31 and 32: Recurrence Set We define Recur 0 0(
Page 33 and 34: Recurrence Set cont. We show S \Att
Page 35 and 36: Büchi games We have shown that Pla
Page 37: Co-Büchi Games Given a Co-Büchi G

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