1. A Decidable Recursive Logic for Weighted Transition Systems Bingtian Xue Aalborg University, DENMARK ICTAC, Sep 18, 2014 Joint work with Kim G. Larsen Radu Mardare

2.  Weighted processes  to express quantitative properties of real systems  the focus is on the weighted behaviors  weighted bisimulation => identical weighted behaviors  Weighted Modal Logics => characterize weighted bisimilarity  Recursion  to encode properties of infinite behaviors: safety, cost-bound liveness Motivation ICTAC, Sep 18, 2014

3.  Properties related to timing and resource constraints Motivation Weighted Transition System ”Complete Proof Systems for Weighted Modal Logic” [TCS13] (Kim Larsen, Radu Mardare) ICTAC, Sep 18, 2014

4. Labeled Weighted System (LWS) ICTAC, Sep 18, 2014

5. Weighted Bisimulation ICTAC, Sep 18, 2014

6. Recursive Weighted Logic (RWL) ICTAC, Sep 18, 2014

7. Recursive Weighted Logic (RWL) ICTAC, Sep 18, 2014

8. Recursive Weighted Logic (RWL) ICTAC, Sep 18, 2014

9. Recursive Weighted Logic (RWL) ICTAC, Sep 18, 2014

10. Recursive Weighted Logic (RWL) ICTAC, Sep 18, 2014

11. Recursive Weighted Logic (RWL) ICTAC, Sep 18, 2014

12. Satisfiability Problem ICTAC, Sep 18, 2014

13. Satisfiability Problem ICTAC, Sep 18, 2014

14. Region Theory ICTAC, Sep 18, 2014

15. Region Theory ICTAC, Sep 18, 2014

16. Region Theory ICTAC, Sep 18, 2014

17. Region Theory ICTAC, Sep 18, 2014

18. Region Theory ICTAC, Sep 18, 2014

19. Satisfiability Problem ICTAC, Sep 18, 2014

20. Satisfiability Problem ICTAC, Sep 18, 2014

21. Satisfiability Problem ICTAC, Sep 18, 2014

22. Satisfiability Problem ICTAC, Sep 18, 2014

23. Satisfiability Problem ICTAC, Sep 18, 2014

24. Satisfiability Problem ICTAC, Sep 18, 2014

25. Conclusion ICTAC, Sep 18, 2014  Conclusion  RWL does not enjoy the finite model property  Satisfiability problem for RWL is decidable  Future work  Extensions of RWL  Axiomatization  Weighted distance

26. Recursive Weighted Logic ICTAC, Sep 18, 2014 Thank you!