Replication and Coordination of State Machines

A single state machine will be as fault-tolerant as the node it is running on. Replicating a state machine on multiple nodes can make it $t$ fault-tolerantA t fault-tolerant system might continue to operate correctly even if more than t nodes fail, but its correct operation cannot be guaranteed beyond failures of t nodes. We need all our replicas to behave similarly for successful replication.

Outputs from replicas

By behaving similarly, we mean producing the same output. All state machines in a group of replicas will produce the same output if the following conditions are satisfied for every replica that runs on a non-faulty node (or processor):

1. Every replica starts in the same initial state.

2. Every replica executes the same requests in the same order.

How many replicas?

Since failures are independent, we will assume that a failure can affect at most one node and (as a result) one state machine. The combined output of an ensemble of replicas resulting from replicating a state machine is the output of its $t$ fault-tolerant state machine.

If nodes can experience Byzantine failures, then for the replica group to be $t$ fault-tolerant, the following must be true:

1. The group must have a minimum of $2t+1$ state machine replicas.

2. The group's output must be the output produced by a majority of the replicas in the group.

As long as the failures are no more than $t$ failures in a $t$ fault-tolerant replica group, we can find out the correct output.

If nodes can only experience fail-stop failures, then we need at least $t+1$ replicas to be t fault-tolerant. Since such nodes only give correct outputs, the output of an ensemble of replicas can be the output of any of its members. With $t$ ...