the byzantine generals problem by luckboy

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```									The Byzantine Generals Problem
Leslie Lamport Microsoft Research

Abstract 1
• 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.

Abstract 2
• 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 discussed.

拜占庭(Byzantine)将军问题
• 拜占庭帝国就是5～15世纪的东罗马帝国，拜占 庭即现在土耳其的伊斯坦布尔。我们可以想象， 拜占庭军队有许多分支，驻扎在敌人城外，每一 分支由各自的将军指挥。将军们只能靠通讯员进 行通讯。在观察了敌人以后，忠诚的将军们必须 制订一个统一的行动计划。然而，这些将军中有 叛徒，他们不希望忠诚的将军们能达成一致，因 而影响统一行动计划的制订与传播。问题是：将 军们必须有一个算法，使所有忠诚的将军们能够 达成一致，而且少数几个叛徒不能使忠诚的将军 们做出错误的计划。

The algorithm guarantee that
• A: All loyal generals decide upon the same plan of action • B: A small number of traitors cannot cause the loyal generals to adopt a bad plan.

• To satisfied A: Every loyal general must obtain the same information v(1), v(2), ……v(n). • If the ith general is loyal, then the value that he sends must be used by every loyal general as the value of v(i)

Byzantine Generals Problem
• A commanding general must send an order to his n-1 lieutenant generals such that 1)All loyal lieutenants obey the same order 2)If the commanding general is loyal, then every loyal lieutenant obeys the order he sends.

Oral Messages
• A1, Every message that is sent is delivered correctly • A2, The receiver of a message knows who sent it. • A3, The absence of a message can be detected.

Problem unsolved

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