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A Note on Consensus on Dual Failure Modes
March 1996 (vol. 7 no. 3)
pp. 225-230

Abstract—Meyer and Pradhan proposed the MS (for "mixed-sum") algorithm to solve the Byzantine Agreement (BA) problem with dual failure modes: arbitrary faults (Byzantine faults) and dormant faults (essentially omission faults and timing faults) [3]. Our study indicates that this algorithm uses an inappropriate method to eliminate the effects of dormant faults and that the bound on the number of allowable faulty processors is overestimated. This paper corrects the algorithm and gives a new bound for the allowable faulty processors.

[1] L. Lamport, R. Shostak, and M. Pease, "The Byzantine Generals Problem," ACM Trans. Programming Languages and Systems, vol. 4, no. 3, July 1982, pp. 382-401.
[2] P. Lincoln and J. Rushby, “A Formally Verified Algorithm for Interactive Consistency Under a Hybrid Fault Model,” Proc. Fault Tolerant Computing Symp. 23, pp. 402–411, Toulouse, France, June 1993.
[3] F.J. Meyer and D.K. Pradhan, "Consensus With Dual Failure Modes," IEEE Trans. Parallel and Distributed Systems, vol. 2, no. 2, pp. 214-222, Apr. 1991.
[4] K. Shin and P. Ramanathan, "Diagnosis of Processors With Byzantine Faults in a Distributed Computing System," IEEE Proc. Symp. Fault-Tolerate Computing, pp. 55-60, 1987.
[5] P.M. Thambidurai and Y.K. Park,"Interactive Consistency with Multiple Failure Modes," Proc. seventh Reliable Dist. Systems Symp., Oct. 1988.

Index Terms:
Byzantine Agreement, consensus problem, distributed systems, dual failure modes, fault tolerance, hybrid fault model.
Hin-Sing Siu, Yeh-Hao Chin, Wei-Pang Yang, "A Note on Consensus on Dual Failure Modes," IEEE Transactions on Parallel and Distributed Systems, vol. 7, no. 3, pp. 225-230, March 1996, doi:10.1109/71.491575
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