A Novel Data-Driven Approach for Generating Verified Loop Invariants

Abstract

Inspired by the procedure that experts construct loop invariants, we propose a novel data-driven approach to generate verified loop invariants automatically. The approach consists of the prediction phase and the evaluation phase. The prediction phase aims to generate candidate loop invariants automatically by solving polynomial equations and synthesizing the extended loop conditions. The evaluation phase aims to generate verified loop invariants that can be utilized to prove the correctness of program postconditions. The spurious candidate invariants are first pruned out using the method of predicate abstraction. Then, the redundant relations are removed from the candidate invariants using an Satisfiability Modulo Theories (SMT) solver. The proposed approach is compared with state-of-the-art methods on 32 benchmarks collected by the recent papers. The experimental results demonstrate that the novel data-driven approach generates 29 verified loop invariants successfully. The proposed approach is efficient at discovering verified loop invariants automatically for executable loop programs. Meanwhile, compared with other methods of generating loop invariants, the proposed approach not only costs less time to generate invariants, but also generates invariants with better quality.