Fixpoint Node Selection Query Languages for Trees

TL;DR

This paper introduces muXPath, an extension of XPath with fixpoint operators, achieving a balance between expressive power and efficient computation for node selection in trees, suitable for web document queries.

Contribution

The paper proposes muXPath, a novel fixpoint extension of XPath, demonstrating its expressive equivalence to MSO and favorable computational properties using automata theory.

Findings

muXPath is as expressive as Monadic Second-Order Logic.

It supports linear-time query evaluation.

It allows exponential-time query containment testing.

Abstract

The study of node selection query languages for (finite) trees has been a major topic in the recent research on query languages for Web documents. On one hand, there has been an extensive study of XPath and its various extensions. On the other hand, query languages based on classical logics, such as first-order logic (FO) or Monadic Second-Order Logic (MSO), have been considered. Results in this area typically relate an XPath-based language to a classical logic. What has yet to emerge is an XPath-related language that is as expressive as MSO, and at the same time enjoys the computational properties of XPath, which are linear time query evaluation and exponential time query-containment test. In this paper we propose muXPath, which is the alternation-free fragment of XPath extended with fixpoint operators. Using two-way alternating automata, we show that this language does combine desired expressiveness and computational properties, placing it as an attractive candidate for the definite node-selection query language for trees.