In this paper, we study the lattice linearity of multiplication and modulo operations. We demonstrate that these operations are lattice linear and the parallel processing algorithms that we study for both these operations are able to exploit the lattice linearity of their respective problems. This implies that these algorithms can be implemented in asynchronous environments, where the nodes are allowed to read old information from each other. 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.

翻译：本文研究了乘法与模运算的格线性性质。我们证明这些运算具有格线性特征，并且针对这两种运算所研究的并行处理算法能够有效利用其各自问题的格线性。这意味着这些算法可部署于异步环境中——允许节点之间读取彼此的陈旧信息。同时，这些算法还展现出快照自稳定特性，即系统从任意初始状态出发，其状态迁移序列严格遵循系统规范。