Towards Directed Collapsibility
Towards Directed Collapsibility
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走向定向可折叠性
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Elizabeth Vidaurre
中科院分区：
文献类型：
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作者：
R. Belton;Robyn Brooks;Stefania Ebli;L. Fajstrup;Brittany Terese Fasy;Catherine Ray;Nicole F. Sanderson;Elizabeth Vidaurre
在有向设置中，固定起始点和终止点之间的有向路径的空间是区分不同有向空间的定义特征。最简单的情况是有向路径的空间同伦等价于单条路径的空间；我们称之为有向路径的平凡空间。拓扑平凡的有向空间可能具有有向路径的非平凡空间，这意味着当忽略这些拓扑空间的方向时，信息就会丢失。我们使用相对于初始或最终顶点的基础有向拓扑空间的有向路径空间，在有向欧几里得立方复形的设置中定义有向可折叠性的概念。此外，我们给出了有向欧几里得立方复形具有从固定初始顶点开始的有向路径的可收缩或连通空间的充分条件。我们还给出了欧几里得立方复形中两个顶点之间的路径空间断开的充分条件。我们的结果可应用于加速并发编程的验证过程和理解并发程序中的部分执行。
In the directed setting, the spaces of directed paths between fixed initial and terminal points are the defining feature for distinguishing different directed spaces. The simplest case is when the space of directed paths is homotopy equivalent to that of a single path; we call this the trivial space of directed paths. Directed spaces that are topologically trivial may have non-trivial spaces of directed paths, which means that information is lost when the direction of these topological spaces is ignored. We define a notion of directed collapsibility in the setting of a directed Euclidean cubical complex using the spaces of directed paths of the underlying directed topological space relative to an initial or a final vertex. In addition, we give sufficient conditions for a directed Euclidean cubical complex to have a contractible or a connected space of directed paths from a fixed initial vertex. We also give sufficient conditions for the path space between two vertices in a Euclidean cubical complex to be disconnected. Our results have applications to speeding up the verification process of concurrent programming and to understanding partial executions in concurrent programs.