Dr. Dobb's Journal - April 2008 - (Page 30)

d04nels_p4ds 2/13/08 10:03 AM Page 30 Core Technology by Mark Nelson The Byzantine Generals Problem An agreement protocol for distributed systems The Byzantine General’s problem is one of many in the field of agreement protocols. In 1982, Mark is a contributing editor to Dr. Dobb’s Journal and author of The Data Compression Book. He can be contacted at http://marknelson.us/. 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. Difficulties This agreement problem doesn’t lend itself to an easy solution. Imagine, for example, that the source process is the only faulty process. It tells half the processes that the value of their order is 0, and the other half that their value is 1. After receiving the order from the source process, the remaining processes have to agree on a value that they will all decide on. The processes could quickly poll one another to see what value they received from the source process. In this scenario, imagine the decision algorithm of a process that receives an initial message of 0 from the source process, but sees that one of the other processes says that the correct value is 1. Given the conflict, the process knows that either the source process is faulty, having given different values to two different peers, or the peer is faulty, and is lying about the value it received from the source process. It’s fine to reach the conclusion that someone is lying, but making a final decision on who is the traitor seems to be an insurmountable problem. And in fact, it can be proven that it is impossible to decide in some cases. The classic example used to show this is when there are only three processes: One source process and two peer processes. In the configurations in Figures 1 and 2, the peer processes attempt to reach consensus by sending each other their proposed value after receiving it from the source process. In Figure 1, the source process (P1) is faulty, sending two different values to the peers. In Figure 2, P3 is faulty, sending an incorrect value to the peer. 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. 30 Dr. Dobb’s Journal l www.ddj.com l April 2008 http://marknelson.us/ http://www.ddj.com

Table of Contents Feed for the Digital Edition of Dr. Dobb's Journal - April 2008

Dr. Dobb's Journal - April 2008 Contents Hmmmm Alia Vox Developer Diaries Dr. Dobb's Excellence in Programming Award Conversations Fast String Search on Multicore Processors The Byzantine Generals Problem Optimizing Math-Intensive Applications with Fixed-Point Arithmetic Random Numbers in a Range Using Generic Programming The Agile Edge Effective Concurrency Swaine's Flames

Dr. Dobb's Journal - April 2008

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