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EECE 396-1 Hybrid and Embedded Systems: Computation

EECE 396-1 Hybrid and Embedded Systems: Computation. T. John Koo, Ph.D. Institute for Software Integrated Systems Department of Electrical Engineering and Computer Science Vanderbilt University 300 Featheringill Hall April 6-15, 2004 john.koo@vanderbilt.edu

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EECE 396-1 Hybrid and Embedded Systems: Computation

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  1. EECE 396-1Hybrid and Embedded Systems: Computation T. John Koo, Ph.D. Institute for Software Integrated Systems Department of Electrical Engineering and Computer Science Vanderbilt University 300 Featheringill Hall April 6-15, 2004 john.koo@vanderbilt.edu http://www.vuse.vanderbilt.edu/~kootj

  2. Analysis: Timed Automata

  3. Topics • Bisimular Transition Systems • Transition Systems • Forward and Backward Reachability Algorithms • Simulation and Bisimulation Relations • Transition Systems and Quotient Transition Systems • Bisimulation between Transition Systems • Bisimulation Algorithm • Bisimulations of Timed Automata • Executions of Timed Automata • Region Equivalent Relation and Partition • Ref: • [1] R. Alur, T.A. Henzinger, and P.-H. Ho. Automatic Symbolic Verification of Embedded Systems. IEEE Transactions on Software Engineering 22:181-201, 1996. • [2] J. Lygeros, Lecture Notes on Hybrid Systems, Cambridge, 2003. • [3] J. Lygeros, C. Tomlin, and S. Sastry, The Art of Hybrid Systems, July 2001.

  4. Analysis: Timed AutomataBisimular Transition Systems

  5. Transition System

  6. Transition System

  7. Transition System

  8. Transition System

  9. Forward and Backward Reachability Algorithms

  10. Forward and Backward Reachability Algorithms

  11. Forward and Backward Reachability Algorithms

  12. Forward and Backward Reachability Algorithms

  13. Simulation and Bisimulation Relations

  14. Simulation and Bisimulation Relations

  15. Simulation and Bisimulation Relations

  16. Simulation and Bisimulation Relations

  17. Simulation and Bisimulation Relations

  18. Simulation and Bisimulation Relations

  19. Simulation and Bisimulation Relations

  20. Simulation and Bisimulation Relations

  21. Simulation and Bisimulation Relations

  22. Simulation and Bisimulation Relations

  23. Bisimulation Algorithm How?

  24. Bisimulation Algorithm

  25. Bisimulation Algorithm

  26. Bisimulation Algorithm

  27. Bisimulation Algorithm

  28. Bisimulation Algorithm

  29. Bisimulation Algorithm

  30. Bisimulation Algorithm

  31. Bisimulation Algorithm

  32. Bisimulation Algorithm

  33. Bisimulation Algorithm

  34. Bisimulation Algorithm

  35. Bisimulation Algorithm

  36. Bisimulation Algorithm

  37. Bisimulation Algorithm

  38. Bisimulation Algorithm

  39. Bisimulation Algorithm

  40. Bisimulation Algorithm

  41. Bisimulation Algorithm

  42. Analysis: Timed AutomataBisimulations of Timed Automata

  43. Timed Automata

  44. Timed Automata

  45. Timed Automata

  46. Timed Automata

  47. Timed Automata

  48. Timed Automata

  49. Timed Automata

  50. Timed Automata

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