乘法与取模算法对异步的容忍性
Tolerance to Asynchrony in Algorithms for Multiplication and Modulo
AI总结：
本文研究了乘法与取模运算的并行算法，证明其状态转换满足格线性，从而使其能在无同步开销的异步环境中正确收敛，并具备快照稳定特性。
摘要：
本文研究了乘法和取模运算的并行处理算法。证明了这些算法下形成的状态转换满足格线性，其中这些算法在全局状态间诱导出一个格。格线性意味着这些算法可在异步环境中实现，允许节点间读取旧信息。这保证了算法无需任何同步开销即可正确收敛。这些算法还表现出快照稳定特性，即从任意状态开始，系统进行的状态转换序列严格遵循其规范。
英文摘要：
In this article, we study some parallel processing algorithms for multiplication and modulo operations. We demonstrate that the state transitions that are formed under these algorithms satisfy lattice-linearity, where these algorithms induce a lattice among the global states. Lattice-linearity implies that these algorithms can be implemented in asynchronous environments, where the nodes are allowed to read old information from each other. It means that these algorithms are guaranteed to converge correctly without any synchronization overhead. These algorithms also exhibit snap-stabilizing properties, i.e., starting from an arbitrary state, the sequence of state transitions made by the system strictly follows its specification.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
