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Lett. 18 (2), 73-76 (1984) The Byzantine Convention includes a system of n processes, some of which may be defective. The problem is that the appropriate processes agree on a binary value issued by an issuer that may itself be one of the processes. If the issuer sends the same value to each process, then all correct processes must agree on that value, but in any case, they must agree on a certain value. An explicit solution without authentication is given for no 3t – 1-process with 2t – 3 rounds and bits of O messages (t3 log t). This solution can be easily extended to the general case of n â©¾ 3t -1 to give a solution with 2t – 3 rounds and O (nt t3 log t) bits of message. We study the problem of obtaining Byzantine agreements in any network where processors and communications are subject to omissions or disruptions. For deterministic and synchronized algorithms, we provide a necessary and sufficient condition that combines problem solving with network connectivity. In particular, we show that an algorithm that resists at most faulty processors and faulty connections that are omitted or shut down is present if and only if the network has a pair of connections (t, k) > (t, k). Okun, M., Barak, A.: On the anonymous Byzantine arrangement. Leibniz Center TR 2004-2, School of Computer Science, The Hebrew University (2004) Pease, M., Shostak, R., Lamport, L.: reaching an agreement in case of error.

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