Generalized Consensus and Paxos

Consensus has been regarded as the fundamental problem that must be solved to implement a fault-tolerant distributed system. However, only a weaker problem than traditional consensus need be solved. We generalize the consensus problem to include both traditional consensus and this weaker version. A straightforward generalization of the Paxos consensus algorithm implements general consensus. The generalizations of consensus and of the Paxos algorithm require a mathematical detour de force into a type of object called a command-structure set.