Amdur ES: On the complexity of the embassy of the Byzantine arrangement. M.S. Thesis, Department of Computer Science, University of Toronto 1988 Amdur, E.S., Weber, S.M. – Hadzilacos, V. On the complexity of the message of the binary Byzantine arrangement in case of crash error. Distrib Comput 5, 175-186 (1992). doi.org/10.1007/BF02277665 Gray JN: The cost of news. In the Proceedings of the 7th ACM Symposium on Principles of Distributed Computing pp 1-7, 1988 If the protocol has the complexity of communication, there must be a $p V node that receives messages from leq f/2. In world 2, the opponent does everything like in world 1, except that (i) it does not damage $p, and (ii) it corrupts all the nodes in $U that have sent messages to $p (this may also contain the specified sender). These damaged nodes do not send messages to $p, but behave honestly with other nodes in $U.

As $p receives 1 `leq f/2` messages, at most the knots $f are damaged in the world 2 (`leq f/2`) and `| V| f/2). This document presents a new Byzantine agreement protocol that tolerates t processor errors with 3t-1 processors, t-o (t) towers, total message bits O (t2) and maximum message size O (t) for each > 0. The protocol is optimal or almost optimal in all cost measurement sizes: the number of processors is optimal, the complexity of the bit is optimal, the number of rounds exceeds the lower limit by o (t), and the maximum size of messages exceeds the lower limit per O (t). The circular complexity is uniformly better than 2 (t-1) and is therefore also for small t. This is the first Byzantine memorandum of understanding that has an optimal complexity of the bit of information. The new protocol is created by the recursive application of a simple but general transformation that changes the number of rounds, the total number of message bits and the maximum size of messages required for a Byzantine agreement protocol, while maintaining accuracy, the number of processor errors tolerated and the total number of processors. Each application of this new transformation reduces the number of bits of messages sent at the expense of adding communication towers. Surprisingly, the basic case of recursive construction is the Memorandum of Understanding from Lamport, Shostak and Pease, which has a series of bits of information exponentially in t.

At a very high level, the Dolev and Resichuk says that if you send few messages < (f/2), then an honest party will receive no message! The party that does not receive any messages has no way of reaching an agreement with the rest. We use a trivial argument of indecision and create a world where a knot $p – no message at all. Therefore, the node of $p and $p cannot tell the difference between a world in which the specified sender sends 0 or a world in which it sends 1. Hadzilacos V, Halpern JY: Optimal new protocols for Byzantine agreements. (1990) Pease M, Shostak R, Lamport L: an agreement in the presence of errors. J ACM 27 (2): 228-234 (1980) Specifically, we prove that any protocol that tolerates up to faulty processes requires at least no-t-1 messages in its flawless execution – and therefore at least [n`t)/2] messages in the worst case and min (P 0.P 1)" (N-t-1) on average, P v being the probability that the value of the bit the sender wants to send is v. We also give protocols that solve the problem using only the minimum number of measures for these three complexity measures. These protocols can be implemented using 1-bit messages. Since a lower limit for the number of messages is also a lower limit for the number of messbits, this means that the narrow limits mentioned above on the number of messages are also narrow limits for the number of messbits. Note: The border is for byzantine mailing (not the Byzantine arrangement).