Distributed architectures are used to improve performance and reliability of various systems. Examples include drone swarms and load-balancing servers. An important capability of a distributed architecture is the ability to reach consensus among all its nodes. Several consensus algorithms have been proposed, and many of these algorithms come with intricate proofs of correctness, that are not mechanically checked. In the controls community, algorithms often achieve consensus asymptotically , e.g., for problems such as the design of human control systems, or the analysis of natural systems like bird flocking. This is in contrast to exact consensus algorithm such as Paxos, which have received much more recent attention in the formal methods community. This paper presents the first formal proof of an asymptotic consensus algorithm, and addresses various challenges in its formalization. Using the Coq proof assistant, we verify the correctness of a widely used consensus algorithm in the distributed controls community, the Weighted-Mean Subsequence Reduced (W-MSR) algorithm . We formalize the necessary and sufficient conditions required to achieve resilient asymptotic consensus under the assumed attacker model. During the formalization, we clarify several imprecisions in the paper proof, including an imprecision on quantifiers in the main theorem.

Understanding and debugging the performance of distributed systems is a notoriously hard task, but a critical one. Traditional techniques like logging, tracing, and benchmarking represent a best-effort way to find performance bugs, but they either require a full deployment to be effective or can only find bugs after they manifest. Even with such techniques in place, real deployments often exhibit performance bugs that cause unwanted behavior. In this paper, we present Performal, a novel methodology that leverages the recent advances in formal verification to provide rigorous latency guarantees for real, complex distributed systems. The task is not an easy one: it requires carefully decoupling the formal proofs from the execution environment, formally defining latency properties, and proving them on real, distributed implementations. We used Performal to prove rigorous upper bounds for the latency of three applications: a distributed lock, ZooKeeper and a MultiPaxos-based State Machine Replication system. Our experimental evaluation shows that these bounds are a good proxy for the behavior of the deployed system and can be used to identify performance bugs in real-world systems.

Safely writing high-performance concurrent programs is notoriously difficult. To aid developers, we introduce Armada, a language and tool designed to formally verify such programs with relatively little effort. Via a C-like language and a small-step, state-machine-based semantics, Armadagives developers the flexibility to choose arbitrary memory layout and synchronization primitives so that they are never constrained in their pursuit of performance. To reduce developer effort, Armadaleverages SMT-powered automation and a library of powerful reasoning techniques, including rely-guarantee, TSO elimination, reduction, and pointer analysis. All of these techniques are proven sound, and Armadacan be soundly extended with additional strategies over time. Using Armada, we verify five concurrent case studies and show that we can achieve performance equivalent to that of unverified code.

Distributed systems are hard to design and implement correctly. Recent work has tried to use formal verification techniques to provide rigorous correctness guarantees. These works present a hard choice, though. One must either opt for the power of refinement-based approaches like IronFleet and Verdi, at the cost of large amounts of manual effort; or choose the more automated approach of I4, IC3PO, SWISS and DistAI which give up the ability to prove refinement and the power and scalability that come with it.

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.