We study time-dependent dynamics on a network of order lattices, where structure-preserving lattice maps are used to fuse lattice-valued data over vertices and edges. The principal contribution is a novel asynchronous Laplacian, generalizing the usual graph Laplacian, adapted to a network of heterogeneous lattices. The resulting gossip algorithm is shown to converge asymptotically to stable "harmonic" distributions of lattice data. This general theorem is applicable to several general problems, including lattice-valued consensus, Kripke semantics, and threat detection, all using asynchronous local update rules.
翻译:我们研究一个按顺序排列的顶点网络上的时间依赖动态, 使用结构保存的拉蒂点地图来将压轴值数据结合到脊椎和边缘上。 主要贡献是一个新的非同步拉板, 概括普通的拉板点图( Laplacian ), 适应一个多式顶点的网络。 结果的八卦算法显示, 将零星地与稳定的拉蒂点数据“ 和谐” 分布相融合。 这个一般性的理论适用于几个一般性问题, 包括以 lattace 估值的共识、 Kripke 语义学和威胁检测, 全部使用无同步的本地更新规则 。