Slide 1

Rahul Sharma, Saurabh Gupta, Bharath Hariharan, Alex Aiken, and Aditya Nori (Stanford, UC Berkeley, Microsoft Research India) Verification as Learning Geometric Concepts

Slide 2

Invariants assume x

Disjunctive invariants assume n > 0; x = 0 ; while ( x < n ) { x = x+1; } assert x = n;

Slide 4

Classification positive examples negative examples + + + + + ++ + +

Slide 5

From invariants to classifiers Safety properties define bad states Invariants separate reachable states from bad states Possible to obtain some examples of states Invariants -> classifiers Examples of reachable/good states -> positive examples Examples of bad states -> negative examples Use a classifier to separate ALL good and bad states

Slide 6

Sample, guess, and check Generate examples of good and bad concrete states Guess an invariant using learner Check if verification succeeds If yes, then done If no, then guess again with more examples Use counter-examples to verification task

Slide 7

Sample good states assume x

From program to data assume x=0 && y