Rahul Sharma, Saurabh Gupta, Bharath Hariharan, Alex Aiken, and Aditya Nori(Stanford, UC Berkeley, Microsoft Research India)Verification as Learning Geometric Concepts1Invariantsassume x 0;x = 0 ;while ( x < n ){ x = x+1;}assert x = n;

3Classification

positive examplesnegative examples+++++++++4From invariants to classifiersSafety properties define bad states

Invariants separate reachable states from bad statesPossible to obtain some examples of states

Invariants -> classifiersExamples of reachable/good states -> positive examplesExamples of bad states -> negative examples

Use a classifier to separate ALL good and bad states5Sample, guess, and checkGenerate examples of good and bad concrete states

Guess an invariant using learner

Check if verification succeedsIf yes, then doneIf no, then guess again with more examplesUse counter-examples to verification task6Sample good statesassume x