1. Husam Abu-Haimed David L. Dill Sergey Berezin
A Refinement Method for Validity Checking of Quantified First-Order Formulas in Hardware Verification
Husam Abu-Haimed
David L. Dill
Sergey Berezin
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2. Outline Problem Definition Predicate Instantiation Heuristic A Example
Heuristic B
Conclusion

3. Problem
Check the validity of

4. Instantiation
To prove
For each find such that:

5. Predicate Instantiation
To prove
Find such that:
Instantiation Predicate 8 m : 8 n : ( m ; n ) ) ( m ; n ) :

6. Predicate Instantiation
Given an Instantiation Predicate
Define:

7. Predicate Instantiation

8. Big Picture Big quantified formula Tiny quantified formula
Quantifier-free formula

9. Heuristic
valid
valid
invalid
From find s.t. :
Repeat

10. Heuristic

11. Deriving
For some there is a
s.t. :
Setting
Will exclude those “bad”

12. Heuristic A

13. Heuristic A

14. Heuristic A

15. Example

16. Example

17. Example

18. Example

19. Example

20. Example

21. Limitations of Heuristic A
Restricted form of
Syntax sensitive:

22. Multiple Instantiation Predicates

23. Multiple Instantiation Predicates

24. Heuristic A’

25. Heuristic B

28. Experiments I : # Integer variables B : # Boolean variables
F : # Finite Domain variables
A : # Unbounded Arrays

29. Future Work New heuristics for instantiation predicates.
Test on other classes of designs.
Compare to other approaches.