A common technique for verifying the safety of complex systems is the inductive invariant method. Inductive invariants are inductive formulas that overapproximate the reachable states of a system and imply a desired safety property. However, inductive invariants are notoriously complex, which makes inductive invariant inference a challenging problem. In this work, we observe that inductive invariant formulas are complex primarily because they must be closed over the transition relation of an entire system. Therefore, we propose a new approach in which we decompose a system into components, assign an assume-guarantee contract to each component, and prove that each component fulfills its contract by inferring a local inductive invariant. The key advantage of local inductive invariant inference is that the local invariant need only be closed under the transition relation for the component, which is simpler than the transition relation for the entire system. Once local invariant inference is complete, system-wide safety follows by construction because the conjunction of all local invariants becomes an inductive invariant for the entire system. We apply our compositional inductive invariant inference technique to two case studies, in which we provide evidence that our framework can infer invariants more efficiently than the global technique. Our case studies also show that local inductive invariants provide modular insights about a specification that are not offered by global invariants.
Dardik et al. (Mon,) studied this question.