This paper studies the Byzantine Agreement problem where the nodes have access to a predictor that flags nodes for suspicion of faulty (Byzantine) behavior. We focus on algorithmic resilience -- the maximum number of faulty nodes an algorithm can tolerate -- and present algorithms and impossibility results whose resilience depend on the accuracy of the predictor. As our first main result, we bring a complete characterization of the consistency--robustness trade-offs in both the non-authenticated and authenticated settings: for $n$ nodes and a parameter $α\in [0, 1]$, we present algorithms that tolerate up to $α\cdot n$ faulty nodes when the predictor is correct (consistency), and up to $\frac{1-α}{2} \cdot n - 1$ faulty nodes when the predictor is arbitrarily wrong (robustness); in the authenticated setting the robustness bound improves to $(1-α) \cdot n - 1$. These trade-offs are exactly tight as we show that one additional faulty node renders the problem impossible. Our second main result characterizes smoothness: the rate at which resilience degrades as the predictor becomes less accurate. We show that resilience linearly decreases in the number of wrong predictions as long as that number stays within a constant fraction of $n$. Concretely, in the non-authenticated setting each additional wrong prediction loses one unit of resilience, whereas in the authenticated setting the decline is halved since two wrong predictions are needed to lose one unit of resilience.

翻译：本文研究节点可访问预测器以标记疑似故障（拜占庭）行为的拜占庭协议问题。我们聚焦于算法弹性——即算法能容忍的最大故障节点数——并提出了其弹性取决于预测器准确性的算法与不可能性结果。作为首个主要结论，我们完整刻画了非认证与认证场景中一致性与鲁棒性之间的权衡：对于 $n$ 个节点及参数 $α\in [0, 1]$，所提算法在预测器正确时（一致性）可容忍最多 $α\cdot n$ 个故障节点，在预测器任意错误时（鲁棒性）可容忍最多 $\frac{1-α}{2} \cdot n - 1$ 个故障节点；在认证场景下，鲁棒性边界提升至 $(1-α) \cdot n - 1$。上述权衡具有精确紧性，因为额外增加一个故障节点即会导致问题不可解。第二个主要结论刻画了平滑性：即弹性随预测器准确性下降而衰减的速率。研究表明，当错误预测数量保持在 $n$ 的常数比例内时，弹性会随错误预测数量线性递减。具体而言，在非认证场景中每增加一个错误预测将损失一个弹性单位，而认证场景中由于需两个错误预测才损失一个弹性单位，弹性衰减速度减半。