A Study of a Positive Fragment of Path Queries: Expressiveness, Normal Form, and Minimization

Abstract

We study the expressiveness of a positive fragment of path queries, denoted Path$\mathstrut^+$, on node-labeled trees documents. The expressiveness of Path$\mathstrut^+$ is studied from two angles. First, we establish that Path$\mathstrut^+$ is equivalent in expressive power to a particular sub-fragment as well as to the class of tree queries, a sub-class of the first-order conjunctive queries defined over label, parent-child, and child-parent predicates. The translation algorithm from tree queries to Path$\mathstrut^+$ yields a normal form for Path$\mathstrut^+$ queries. Using this normal form, we can decompose a Path$\mathstrut^+$ query into sub-queries that can be expressed in a very small sub-fragment of Path$\mathstrut^+$ for which efficient evaluation strategies are available. Second, we characterize the expressiveness of Path$\mathstrut^+$ in terms of its ability to resolve nodes in a document. This result is used to show that each tree query can be translated to a unique, equivalent, and minimal tree query. The combination of these results yields an effective strategy to evaluate a large class of path queries on documents.