lecture9-extra_slides_Buchi_game

# lecture9-extra_slides_Buchi_game - LTL control for...

This preview shows pages 1–6. Sign up to view the full content.

LTL control for non-deterministic transition systems

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 )
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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)
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!!

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern