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The Byzantine Generals Problem July 1982

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Reliable computer systems must handle malfunctioning components that give conflicting information
to different parts of the system. This situation can be expressed abstractly in terms of a group of
generals of the Byzantine army camped with their troops around an enemy city. Communicating only
by messenger, the generals must agree upon a common battle plan. However, one or more of them
may be traitors who will try to confuse the others. The problem is to find an algorithm to ensure that
the loyal generals will reach agreement. 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. With unforgeable written messages, the problem is solvable for any number of
generals and possible traitors. Applications of the solutions to reliable computer systems are then
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