1. Rahul Sharma Joint work with Aditya Nori (MSR India) and Alex Aiken (Stanford)

3. x y

5. Is there a connection?

8.  Unroll the loops  Find interpolants  Get general proofs (loop invariants)  Get positive and negative examples  Find a classifier  Get a predicate which generalizes

9. positive examples negative examples + + + + +

10. Separators All separators are good candidates for interpolants + ++ + +

11. Optimal Margin Classifier + + + +

12. x = y = 0; while(*) x++; y++; while(x != 0) x--; y--; assert (y == 0); x = y = 0; if(*) x++; y++; p: if(x != 0) x--; y--; if(x == 0) assert (y == 0);

13. x y (0,0) + + (1,1)

15.  Data is not linearly separable  The candidate interpolant is not an interpolant x y + +

16. x y (0,0) + + (1,1)(0,1) (1,0)

18. x y (0,0) + + (1,1) Interpolant!

19.  1000 lines of C++  LIBSVM for SVM queries  Z3 theorem prover

21.  Interpolants used in tools  BLAST, IMPACT …  Interpolants from proofs  Krajícek[97], Pudlák[97], McMillan[05], …  Interpolants from constraint solving  ARMC, Rybalchenko et al. [07]

22.  Connect interpolants and classifiers  A sound interpolation procedure  Future work: non-linear interpolants  Integrate with a verification tool  EUF, arrays, bit-vectors, etc.