A layered analysis of consensus

This paper introduces a simple notion of layering as a tool for analyzing well-behaved runs of a given model of distributed computation. Using layering, a model-independent analysis of the consensus problem is performed and then applied to proving lower bounds and impossibility results for consensus in a number of familiar and less familiar models. The proofs are simpler and more direct than existing ones, and they expose a unified structure to the difficulty of reaching consensus. In particular, the proofs for the classical synchronous and asynchronous models now follow the same outline. A new notion of connectivity among states in runs of a consensus protocol, called potence connectivity, is introduced. This notion is more general than previous notions of connectivity used for this purpose and plays a key role in the uniform analysis of consensus.