Completeness and Decidability Properties for Functional Dependencies in XML

TL;DR

This paper investigates the logical properties of functional dependencies in XML, proving axioms' completeness for unary cases and presenting a linear-time algorithm for implication decision problems.

Contribution

It establishes the completeness of axioms for unary XML functional dependencies and provides a linear-time decision algorithm for their implication problem.

Findings

Axioms are complete for unary XML functional dependencies.

Implication problem for unary XFDs is decidable.

A linear-time algorithm for implication checking is developed.

Abstract

XML is of great importance in information storage and retrieval because of its recent emergence as a standard for data representation and interchange on the Internet. However XML provides little semantic content and as a result several papers have addressed the topic of how to improve the semantic expressiveness of XML. Among the most important of these approaches has been that of defining integrity constraints in XML. In a companion paper we defined strong functional dependencies in XML(XFDs). We also presented a set of axioms for reasoning about the implication of XFDs and showed that the axiom system is sound for arbitrary XFDs. In this paper we prove that the axioms are also complete for unary XFDs (XFDs with a single path on the l.h.s.). The second contribution of the paper is to prove that the implication problem for unary XFDs is decidable and to provide a linear time algorithm for it.