Automatic loop-invariant generation anc refinement through selective sampling

Automatic loop-invariant generation is important in program analysis and verification. In this paper, we propose to generate loop-invariants automatically through learning and verification. Given a Hoare triple of a program containing a loop, we start with randomly testing the program, collect program states at run-time and categorize them based on whether they satisfy the invariant to be discovered. Next, classification techniques are employed to generate a candidate loop-invariant automatically. Afterwards, we refine the candidate through selective sampling so as to overcome the lack of sufficient test cases. Only after a candidate invariant cannot be improved further through selective sampling, we verify whether it can be used to prove the Hoare triple. If it cannot, the generated counterexamples are added as new tests and we repeat the above process. Furthermore, we show that by introducing a path-sensitive learning, i.e., partitioning the program states according to program locations they visit and classifying each partition separately, we are able to learn disjunctive loop-invariants. In order to evaluate our idea, a prototype tool has been developed and the experiment results show that our approach complements existing approaches.