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。我们证明了这些运算具有格线性特征，并且所研究的两种并行处理算法能够利用各自问题中的格线性特性。这意味着这些算法可在异步环境中实现——在该环境中允许节点相互读取旧信息。这些算法还展现出快照稳定特性，即从任意初始状态开始，系统进行的状态转换序列严格遵循其规范。