1. Real-Time Systems, COSC-4301-01, Lecture 18
Stefan Andrei
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COSC , Lecture 18

2. Reminder of the last lecture
Model checking of finite-state systems
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3. Overview of This Lecture
Symbolic model checking of finite-state systems
(Ordered) Binary Decision Diagrams
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4. Boolean functions
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5. Representing boolean functions
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6. Binary decision trees
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7. Problems
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8. Binary decision diagrams (BDDs)
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9. Reduction rules
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10. Reduction rules (cont)
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11. Variable ordering
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12. Summary of reduction rules
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13. Operations on BDDs
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14. Predicates
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15. Equivalence of functions
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16. Operations
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17. Ordered BDDs (OBDDs)
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18. Properties of OBBDs
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19. Properties of reduced OBBDs
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20. Properties of reduced OBBDs (cont)
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21. OBBDs and variable ordering
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22. Reduction for OBDDs
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23. Labeling algorithm Mistake: Label all 0’s with 0. 10/23/2019
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24. Labeling algorithm
3. If there is a node m with the same variable as n such that l(n)=l(m) and h(n)=h(m), label n with m’s label.
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25. Complexity
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26. Summary Symbolic model checking of finite-state systems
(Ordered) Binary Decision Diagrams
Models and modelling (analysis & design models)
A model is totality of information to describe the 5 views
Methodologies = defines a number of models that can be used to develop a system
= Examples (structured methods, OO methods)
= Formal notations (OO model = UML)
UML = unification of earlier OO modelling languages
Design models and code (the models used in the design of a system present an abstract view of it, and an implementation adds enough detail to make these models executable).
The software development process (Unified Process)
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COSC , Lecture 18

27. Reading suggestions Chapter 4 of [Cheng; 2002]
Chapter 6 of [Huth and Ryan; 2004], where this is:
M. Huth and M. Ryan: Logic in Computer Science. Modelling and Reasoning about Systems. Cambridge University Press, 2004, ISBN
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28. Coming up next
Visual formalism, statecharts, and STATEMATE (Chapter 5 of [Cheng; 2002])
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29. Thank you for your attention! Questions?
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COSC , Lecture 18