树上关系代数导航表达的结构刻画
Structural characterizations of the navigational expressiveness of relation algebras on a tree
摘要：
给定一个文档D在一个无序的节点标记树的形式，我们研究的表达D的各种基本片段的XML文档的核心导航语言。工作的角度来看，这些语言的塔斯基的关系代数的片段，我们给出的特征，在D的结构方面，当一个二元关系的节点是可定义的表达在这些代数。由于在这样的关系中的每对节点代表D中的唯一路径，因此我们的结果捕获了D中可定义在每个片段中的路径集合。我们把这种语言语义学的观点称为“全局观”。与这种全局视图相反，还有一种“局部视图”，在这种视图中，人们对可以从文档中的特定节点开始导航到的节点感兴趣。在这个观点中，我们刻画了D中的一组节点何时可以被定义为将表达式应用于D的给定节点的结果。所有这些可定义性的结果，无论是在全球和本地的视图中，通过使用一个强大的两步方法，它包括第一次表征时，两个节点不能区分的表达在各自的片段中的bandwidth，然后引导这些表征所需的结果。
英文摘要：
Given a document D in the form of an unordered node-labeled tree, we study the expressiveness on D of various basic fragments of XPath, the core navigational language on XML documents. Working from the perspective of these languages as fragments of Tarski's relation algebra, we give characterizations, in terms of the structure of D, for when a binary relation on its nodes is definable by an expression in these algebras. Since each pair of nodes in such a relation represents a unique path in D, our results therefore capture the sets of paths in D definable in each of the fragments. We refer to this perspective on language semantics as the "global view." In contrast with this global view, there is also a "local view" where one is interested in the nodes to which one can navigate starting from a particular node in the document. In this view, we characterize when a set of nodes in D can be defined as the result of applying an expression to a given node of D. All these definability results, both in the global and the local view, are obtained by using a robust two-step methodology, which consists of first characterizing when two nodes cannot be distinguished by an expression in the respective fragments of XPath, and then bootstrapping these characterizations to the desired results.
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