Comparing Downward Fragments of the Relational Calculus with Transitive Closure on Trees

TL;DR

This paper analyzes the expressive power of downward navigational query languages on trees, examining how adding features like transitive closure and intersection affects their capabilities and closure properties.

Contribution

It provides a complete hierarchy (Hasse diagram) of the expressive power of various query language fragments on trees, including their closure properties.

Findings

Complete hierarchy of expressive power for query fragments

Identification of closure properties under difference and intersection

Analysis of effects of adding transitive closure and other operators

Abstract

Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations using composition and union. We study the effects on relative expressiveness when we add transitive closure, projections, coprojections, intersection, and difference; this for boolean queries and path queries on labeled and unlabeled structures. In all cases, we present the complete Hasse diagram. In particular, we establish, for each query language fragment that we study on trees, whether it is closed under difference and intersection.