lecture9-extra_slides_Buchi_game

lecture9-extra_slides_Buchi_game - LTL control for...

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LTL control for non-deterministic transition systems
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We have : A non-deterministic transition system (model for our system) An LTL formula φ over set Π (desired property) 0 ( , , , , , ) T Q Q h δ = Σ q 1 q 2 q 4 q 3 2 1 σ 1 1 σ 2 3 σ 4 4 σ 1 (2 4) σ 3 3 σ Simplifying assumption: Identity observation map h ( Π = Q )
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a) Cut all non-deterministic transitions (do not allow inputs producing non-determinism) b) Try to get a run satisfying the formula (as in previous approach) Simple , but too conservative approach 2 4 ( ) q q q 1 q 2 q 4 q 3 2 1 σ 1 1 σ 2 3 σ 4 4 σ 3 3 σ q 1 q 2 q 4 q 3 2 1 σ 1 1 σ 2 3 σ 4 4 σ 1 (2 4) σ 3 3 σ A simple approach
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A better approach 1 q 2 q 3 q 4 q 5 q 4 q adversary player LTL games on graphs : Thomas, W.: Infinite games and verification. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 58–64. Springer, Heidelberg (2002) Wallmeier, N., H ¨ utten, P., Thomas, W.: Symbolic synthesis of finite-state controllers for request-response specifications. In: H. Ibarra, O., Dang, Z. (eds.) CIAA 2003. LNCS, vol. 2759, pp. 113–127. Springer, Heidelberg (2003) Piterman, N., Pnueli, A., Sa’ar, Y.: Synthesis of reactive(1) designs. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 364–380. Springer, Heidelberg (2005)
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A better approach 1 q 2 q 3 q 4 q 5 q 4 q adversary player LTL games on graphs : Works only if the corresponding Buchi automaton is deterministic!!
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