Abstract
The problem of fault-tolerant agreement is fundamental to distributed computing. When agreement is to be reached in spite of arbitrary behavior by faulty processors, this problem is called Distributed Consensus. By requiring that the number of faulty processors be O(√n), where n is the number of processors in the system, we are able to derive two new protocols for Distributed Consensus. Both are simple and use messages that are only one bit in length, and both provide for early stopping: the fewer failures there are, the fewer rounds of communication are required. One protocol is optimal with respect to the number of rounds of communication required, and the other is asymptotically optimal with respect to the total number of message bits exchanged.
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