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The Byzantine Generals Problem describes how distributed participants can agree on a decision even when some may lie, behave arbitrarily, or send conflicting messages. In the original oral-message model, agreement is possible if and only if more than two-thirds of the participants are loyal.
What the Byzantine Generals Problem means
It is a distributed agreement problem under adversarial behavior. Each participant needs to reach a consistent decision, although some participants may provide misleading information or tell different participants different things. The “generals” are a memorable analogy for distributed computers or other units that need to coordinate.
NIST’s Dictionary of Algorithms and Data Structures describes the problem as consensus among distributed units when some give misleading answers.
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In their 1982 paper, Leslie Lamport, Robert Shostak, and Marshall Pease state: “It is shown that, using only oral messages, this problem is solvable if and only if more than two-thirds of the generals are loyal; so a single traitor can confound two loyal generals.” The result applies to the paper’s oral-message model; it is not a universal threshold for every consensus protocol.
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Expressed in terms of faults, that condition means fewer than one-third of participants may be traitors in this model. At exactly one-third, the requirement that more than two-thirds be loyal is not met. The original paper’s record and abstract are available from SRI International; Microsoft Research lists the paper’s publication details in its publication record.
Why this is not the Two Generals Problem
The two problems concern different kinds of uncertainty. The Two Generals Problem asks whether separated parties can coordinate when messages may fail to arrive. The Byzantine Generals Problem asks whether participants can agree when some participants may lie or send inconsistent messages. NIST discusses the Byzantine problem separately from the two-general messenger-loss scenario.
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How to read claims about Byzantine fault tolerance
Questions such as “How many Byzantine faults can a system tolerate?” depend on the system’s protocol and assumptions. The more-than-two-thirds loyal result belongs to the original oral-message setting. A familiar expression such as 3f + 1 nodes is associated with a strict less-than-one-third fault threshold in common Byzantine fault-tolerance settings, but the expression alone does not establish what a particular implementation tolerates. Check the protocol’s assumptions about message authentication, timing, communication reliability, and faulty participants before applying the original result to a real system.
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Leslie Lamport, Robert Shostak, and Marshall Pease published “The Byzantine Generals Problem” in ACM Transactions on Programming Languages and Systems, volume 4, issue 3, in July 1982, pages 382–401. The generals story made a central distributed-computing problem easier to remember; it is an analogy, not a claim about military history.
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