Formal analyses of blockchain protocols have received much attention recently. Consistency results of Nakamoto's blockchain protocol are often expressed in a quantity $c$, which denotes the expected number of network delays before some block is mined. With $\mu$ (resp., $\nu$) denoting the fraction of computational power controlled by benign miners (resp., the adversary), where $\mu + \nu = 1$, we prove for the first time that to ensure the consistency property of Nakamoto's blockchain protocol in an asynchronous network, it suffices to have $c$ to be just slightly greater than $\frac{2\mu}{\ln (\mu/\nu)}$. Such a result is both neater and stronger than existing ones. In the proof, we formulate novel Markov chains which characterize the numbers of mined blocks in different rounds.

中文翻译：

---

异步网络中区块链一致性的分析：导出一个整洁的边界

区块链协议的正式分析最近备受关注。Nakamoto 的区块链协议的一致性结果通常以数量 $c$ 表示，这表示在挖掘某个区块之前网络延迟的预期数量。$\mu$ (resp., $\nu$) 表示由良性矿工（resp.，对手）控制的计算能力的一部分，其中 $\mu + \nu = 1$，我们首次证明为了确保中本聪区块链协议在异步网络中的一致性属性，只要让 $c$ 略大于 $\frac{2\mu}{\ln (\mu/\nu)}$ 就足够了。这样的结果比现有的更整洁、更强大。在证明中，我们制定了新的马尔可夫链，它表征了不同轮次中挖掘的块的数量。