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Consensus With Dual Failure Modes
April 1991 (vol. 2 no. 2)
pp. 214-222

The problem of achieving consensus in a distributed system is discussed. Systems aretreated in which either or both of two types of faults may occur: dormant (essentiallyomission and timing faults) and arbitrary (exhibiting arbitrary behavior, commonly referred to as Byzantine). Previous results showed that are number of dormant faults may be tolerated when there are no arbitrary faults and that, at most, (n-1/3) arbitrary faults may be tolerated when there are no dormant faults (n is the number of processors). Acontinuum is established between the previous results: an algorithm exists if n(f/submax/+2m/sub max/) and c(f/sub max/+m/sub max/) (where c is the system connectivity),when faults are constrained so that there are at most f/sub max/ and at most m/submax/ of these that are arbitrary. An algorithm is given and compared to known algorithms. A method is given to establish virtual links so that the communications graph appears completely connected.

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Index Terms:
Index Termsconsensus; distributed system; arbitrary behavior; Byzantine; dormant faults; arbitraryfaults; communications graph; distributed processing; fault tolerant computing
F.J. Meyer, D.K. Pradhan, "Consensus With Dual Failure Modes," IEEE Transactions on Parallel and Distributed Systems, vol. 2, no. 2, pp. 214-222, April 1991, doi:10.1109/71.89066
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