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 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAAAAAA

Outline Problem Definition Predicate Instantiation Heuristic A Example Heuristic B Conclusion

Problem Check the validity of

Instantiation To prove For each find such that:

Predicate Instantiation To prove Find such that: Instantiation Predicate 8 ® m : 8 ¯ n : © ( ® m ; ¯ n ) ) ª ( ® m ; ¯ n ) :

Predicate Instantiation Given an Instantiation Predicate Define:

Predicate Instantiation

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

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

Heuristic

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

Heuristic A

Heuristic A

Heuristic A

Example

Example

Example

Example

Example

Example

Limitations of Heuristic A Restricted form of Syntax sensitive:

Multiple Instantiation Predicates

Multiple Instantiation Predicates

Heuristic A’

Heuristic B

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

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