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	TABLE OF CONTENTS Byzantine Generals Difficulties The Lamport, Pease, and Shostak Algorithm The First Stage The Second Stage A More Complicated Example

The Byzantine General's problem is one of many in the field of agreement protocols. In 1982, Leslie Lamport described this problem in a paper written with Marshall Pease and Robert Shostak. Lamport framed the paper around a story problem after observing what he felt was an inordinate amount of attention received by Dijkstra's Dining Philosopher problem.

This problem is built around an imaginary General who makes a decision to attack or retreat, and must communicate the decision to his lieutenants. A given number of these actors are traitors (possibly including the General). Traitors cannot be relied upon to properly communicate orders; worse yet, they may actively alter messages in an attempt to subvert the process.

The generals are collectively known as processes. The general who initiates the order is the source process, and the orders sent to the other processes are messages. Traitorous generals and lieutenants are faulty processes, and loyal generals and lieutenants are correct processes. The order to retreat or attack is a message with a 1 or 0.

In general, a solution to agreement problems must pass three tests: termination, agreement, and validity. As applied to the Byzantine General's problem, these three tests are:

• A solution has to guarantee that all correct processes eventually reach a decision regarding the value of the order they have been given.
• All correct processes have to decide on the same value of the order they have been given.
• If the source process is a correct process, all processes have to decide on the value that was originally given by the source process.

One side effect of this is that if the source process is faulty, all other processes still have to agree on the same value. It doesn't matter what value they agree on, they simply all have to agree. So if the General is subversive, all lieutenants still have to come to a common, unanimous decision.

1 Byzantine Generals | 2 Difficulties | 3 The Lamport, Pease, and Shostak Algorithm | 4 The First Stage | 5 The Second Stage | 6 A More Complicated Example Next Page

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