Round Complexity and Communication Complexity Sample Clauses

Round Complexity and Communication Complexity. The first honest leader will ensure termination. The random leader election subroutine ensures a (ƒ + 1)/(2ƒ + 1) > 1/2 probability that each leader is honest, so the core protocol terminates in expected 2 iterations, plus one extra round to forward ƒ + 1 notify. Thus, if an iteration requires r rounds, our core protocol requires 2r + 1 rounds to terminate in expectation. If the adversary is adaptive and strongly xxxxxxx, each iteration requires r = 7 rounds. If the adversary is adaptive and normal xxxxxxx, the elect round can happen in parallel to propose, and each iteration has r = 6 rounds. If the adversary is static (xxxxxxx or otherwise), we do not need the two prepare rounds, and the elect round can happen in parallel to either status or propose, giving r = 4 rounds per iteration. Next, we analyze the communication complexity. We will show that each round consumes O(n2) communication. Hence, the core protocol requires expected O(n2) communication (whether the adversary is adaptive or static, xxxxxxx or not). First of all, note that although a certificate consists of ƒ + 1 signatures, its size can be reduced to a single signature using threshold signatures [8, 21, 28, 37].
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Round Complexity and Communication Complexity. The first honest leader will ensure termination. The random leader election subroutine ensures a (f + 1)/(2f +

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