Designing and implementing distributed systems correctly is a very challenging task. Recently, formal verification has been successfully used to prove the correctness of distributed systems. At the heart of formal verification lies a computerchecked proof with an inductive invariant. Finding this inductive invariant, however, is the most difficult part of the proof. Alas, current proof techniques require inductive invariants to be found manually—and painstakingly—by the developer. In this paper, we present a new approach, Incremental Inference of Inductive Invariants (I4), to automatically generate inductive invariants for distributed protocols. The essence of our idea is simple: the inductive invariant of a finite instance of the protocol can be used to infer a general inductive invariant for the infinite distributed protocol. In I4, we create a finite instance of the protocol; use a model checking tool to automatically derive the inductive invariant for this finite instance; and generalize this invariant to an inductive invariant for the infinite protocol. Our experiments show that I4 can prove the correctness of several distributed protocols like Chord, 2PC and Transaction Chains with little to no human effort.

Despite several decades of research, the problem of formal verification of infinite-state systems has resisted effective automation. We describe a system — Ivy — for interactively verifying safety of infinite-state systems. Ivy’s key principle is that whenever verification fails, Ivy graphically displays a concrete counterexample to induction. The user then interactively guides generalization from this counterexample. This process continues until an inductive invariant is found. Ivy searches for universally quantified invariants, and uses a restricted modeling language. This ensures that all verification conditions can be checked algorithmically. All user interactions are performed using graphical models, easing the user’s task. We describe our initial experience with verifying several distributed protocols.