AI 中文总结
介绍用于平移不变全序的计算软件包TITO_Explore，定义规范窗口表示法，设计实现相关算法，能归一化窗口表示法、计算逆序集、比较弱序及计算并，弱序比较算法通过划分子集操作，并用加权有向图解决并的计算问题。
AI 中文摘要
我们引入了TITO_Explore，这是一个用于表示和计算平移不变全序（TITOs）的软件包。我们为TITOs定义了一种规范窗口表示法，并设计和实现了涉及它们的几个计算任务的算法。该软件包将给定TITO的窗口表示法归一化为其规范形式，计算其逆序集，比较两个TITOs之间的弱序，并计算两个指定TITOs的并。我们的弱序比较算法通过将逆序集划分为不相交子集来操作，从而将比较问题分解为对子集对的评估。并算法使用边加权有向图来表示逆序，并将找到并的问题转换为图中的加权路径问题。
英文摘要
We introduce TITO_Explore, a software package for representing and computing with Translation-Invariant Total Orders (TITOs). We define a canonical window notation for TITOs and design and implement algorithms for several computational tasks involving them. The package normalizes the window notation of a given TITO into its canonical form, computes its inversion set, compares the weak order between two TITOs, and computes the join of two specified TITOs. Our weak order comparison algorithm operates by partitioning the inversion sets into disjoint subsets, thereby breaking down the comparison problem into evaluations of paired subsets. The join algorithm uses an edge-weighted directed graph to represent inversions and converts the problem of finding the join into a weighted path problem in the graph.
Comments13 pages
