Difficulty algorithms are a fundamental component of Proof-of-Work blockchains, aimed at maintaining stable block production times by dynamically adjusting the network difficulty in response to the miners' constantly changing computational power. Targeting stable block times is critical, as this ensures consistent transaction throughput. Some blockchains need difficulty algorithms that react quickly to severe hash rate fluctuations. However, without careful design this could create vulnerabilities that incentivize miners to engage in coin-hopping strategies which yield an unreliable system due to unstable processing of transactions. We provide an empirical analysis of how Bitcoin Cash exhibits cyclicality in block solve times as a consequence of a positive feedback loop in its difficulty algorithm design. Additionally, we examine the extent to which miners' behavior contributes towards this phenomenon over time. In response, we mathematically derive a difficulty algorithm based on a negative exponential filter that prohibits the formation of positive feedback loops and exhibits additional desirable properties, such as history agnosticism. We compare the described algorithm to that of Bitcoin Cash in a simulated mining environment and verify that the former would eliminate the severe oscillations in block solve times. Lastly, we outline how this model can more generally replace difficulty algorithms in other Proof-of-Work blockchains.

中文翻译：

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不稳定的吞吐量：当难度算法崩溃时

难度算法是工作量证明区块链的基本组成部分，旨在通过动态调整网络难度以响应矿工不断变化的计算能力来维持稳定的区块生产时间。以稳定的区块时间为目标至关重要，因为这可确保一致的交易吞吐量。一些区块链需要对严重的哈希率波动做出快速反应的难度算法。然而，如果没有精心设计，这可能会产生漏洞，激励矿工参与跳币策略，由于交易处理不稳定，这些策略会产生不可靠的系统。我们对比特币现金如何由于其难度算法设计中的正反馈循环而在块求解时间中表现出周期性进行了实证分析。此外，我们研究了随着时间的推移，矿工行为对这种现象的影响程度。作为回应，我们从数学上推导出一种基于负指数滤波器的难度算法，该算法禁止形成正反馈循环并表现出额外的理想属性，例如历史不可知论。我们将所描述的算法与模拟采矿环境中的比特币现金算法进行比较，并验证前者将消除块求解时间的严重振荡。最后，我们概述了该模型如何更普遍地替代其他工作量证明区块链中的难度算法。我们在数学上推导出一种基于负指数滤波器的难度算法，该算法禁止形成正反馈回路并表现出额外的理想特性，例如历史不可知论。我们将所描述的算法与模拟采矿环境中的比特币现金算法进行比较，并验证前者将消除块求解时间的严重振荡。最后，我们概述了该模型如何更普遍地替代其他工作量证明区块链中的难度算法。我们在数学上推导出一种基于负指数滤波器的难度算法，该算法禁止形成正反馈回路并表现出额外的理想特性，例如历史不可知论。我们将所描述的算法与模拟采矿环境中的比特币现金算法进行比较，并验证前者将消除块求解时间的严重振荡。最后，我们概述了该模型如何更普遍地替代其他工作量证明区块链中的难度算法。