A Simple Proof of a Simple Consensus Algorithm

We present a proof of a simple consensus algorithm. The algorithm is known [1]; the proof style is new. It is difficult to reason about communicating processes when some of them may fail. We show that representing the algorithm at a higher level—using equations only—permits us to treat failures in a formal manner. This approach was first utilized in Chandy and Misra [1988, Chapter 18] for proving the correctness of an unauthenticated Byzantine Agreement protocol due to Dolev et al. [1982], and Srikanth and Toueg [1987], for the case when the number of reliable processes is more than twice the number of unreliable processes; this paper deals with a simpler problem—the number of reliable processes exceeds thrice the number of unreliable processes—which has a simpler algorithm.