Developing a Consensus Algorithm Using Stepwise Refinement

Abstract

Consensus problems arise in any area of computing where distributed processes must come to a joint decision. Although solutions to consensus problems have similar aims, they vary according to the processor faults and network properties that must be taken into account, and modifying these assumptions will lead to different algorithms. Reasoning about consensus protocols is subtle, and correctness proofs are often informal. This paper gives a fully formal development and proof of a known consensus algorithm using the stepwise refinement method Event-B. This allows us to manage the complexity of the proof process by factoring the proof of correctness into a number of refinement steps, and to carry out the proof task concurrently with the development. During the development the processor faults and network properties on which the development steps rely are identified. The research outlined here is motivated by the observation that making different choices at these points may lead to alternative algorithms and proofs, leading to a refinement tree of algorithms with partially shared proofs.