Formal Verification of Consensus Algorithms Tolerating Malicious Faults

Abstract

Abstract. Consensus is the paradigmatic problem in fault-tolerant distributed computing: it requires network nodes that communicate by message passing to agree on common value even in the presence of (benign or malicious) faults. Several algorithms for solving Consensus exist, but few of them have been rigorously verified, much less so formally. The Heard-Of model proposes a simple, unifying framework for defining distributed algorithms in the presence of communication faults. Algorithms proceed in communication-closed rounds, and assumptions on the faults tolerated by the algorithm are stated abstractly in the form of communication predicates. Extending previous work on the case of benign faults, our approach relies on the fact that properties such as Consensus can be verified over a coarse-grained, round-based representation of executions. We have encoded the Heard-Of model in the interactive proof assistant Isabelle/HOL and have used this encoding to formally verify three Consensus algorithms based on synchronous and asynchronous assumptions. Our proofs give some new insights into the correctness of the algorithms, in particular with respect to transient faults.

Communication-Closed Layers as Paradigm for Distributed Systems: A Manifesto

“…Such systems can be effectively verified with different methods. In the literature, we already find results using the following methods: a domain-specific consensus logic with decision procedures [11], [12], and methods to infer invariants [47], cut-off results [35], for model checking abstraction-based model checking [1], bounded model checking [45], [44], interactive theorem provers and finite state model checking [7], [8].…”

A Logic-Based Framework for Verifying Consensus Algorithms

“…Overview: Let us consider the formula in (9), stating that no process decided before applying the transition relation TR given in (4), and afterwards two processes decide on different values:…”

“…For instance, Isabelle has been used to verify algorithms in the heard-of model [9]. The verification of distributed systems has also been tackled using the TLA+ specification language [18].…”

A Mechanized Model for CAN Protocols

“…His work relies on previous notable efforts, such as a rigorous approach to describe network protocols [16], a formal model of the OCaml programming language, and an operational verification of OCaml code. Charron-Bost and Merz [3] formally verified a modified version of the Paxos consensus algorithm using Isabelle/HOL. They modeled the consensus algorithm using the Heard-Of model (HO), a round-based computational model for fault-tolerant distributed systems.…”