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

We study the expressiveness of a positive fragment of path queries, denoted Path
⁺
, on documents that can be represented as node-labeled trees. The expressiveness of Path
⁺
is studied from two angles. First, we establish that Path
⁺
is equivalent in expressive power to two particular subfragments, as well as to the class of tree queries, a subclass of the first-order conjunctive queries defined over the label, parent–child and child–parent predicates. The translation algorithm from tree queries to Path
⁺
yields a normal form for Path
⁺
queries. Using this normal form, we can decompose a Path
⁺
query into subqueries that can be expressed in a very small fragment of Path
⁺
for which efficient evaluation strategies are available. Second, we characterize the expressiveness of Path
⁺
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.