I am often wrongly credited with inventing the problem of Byzantine arrangement. The problem was formulated by people who worked on SIFT (see ) before I arrived at SRI. I had already discovered and written the problem of Byzantine errors . (I don`t know if it was before or at the same time as his discovery at SRI.) However, people at SRI had a much simpler and more elegant statement about the problem than there were in . Prior to this paper, it was generally thought that a three-processor system could tolerate a defective processor. This document shows that “Byzantine” errors in which a faulty processor sends inconsistent information to other processors can defeat any conventional three-processor algorithm. (The Byzantine term only appeared .) In general, 3n-1 processors are needed to tolerate n errors. However, when digital signatures are used, 2n-1 processors are sufficient. This document presented the problem of managing Byzantine errors. I think it also contains the first specific explanation of the problem of consensus. We present networks of a limited degree and a fully polynomid scheme agreed almost everywhere, which is very likely to tolerate faulty processors located at random, where processors are independent with a constant probability.
This work was partially sponsored by Computational Logic, Inc. of the National Aeronautics and Space Administration Langley Research Center (NAS1-18878). The opinions and conclusions contained in this document are those of the authors and should not be construed as representing the official, either explicit or implied, guidelines of Computational Logic, Inc., NASA Langley Research Center or the U.S. government. We thank our NASA sponsors, especially Ricky Butler, for providing invaluable advice on the formulation of this problem and our colleagues at Computational Logic for building and maintaining a wonderful research environment. Over the years, I have often wondered if the people who actually build planes are aware of the problem of Byzantine breakdowns. In 1997, I received an email from John Morgan, who used to work at Boeing. He told me that he came across our work in 1986 and that the people who build passenger planes at Boeing are aware of the problem and design their systems accordingly. But in the late 1980s and early 1990s, the People at Boeing who worked on military aircraft and the space station did not understand the problem, and the people at McDonnell-Douglas did not understand the problem. I have no idea what Airbus knows or when they knew it.
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