The Implication Problem for Functional Dependencies in Complete Xml Documents

With the growing use of XML as a format for the permanent storage of data, the study of functional dependencies in XML (XFDs) is of fundamental importance in understanding how to effectively design XML databases without redundancy or update problems. We investigate a central problem in dependency theory, that of determining when a set of XFDs logically implies another XFD in the context of XML documents with no missing information. The first contribution of the article is to provide an axiom system for XFD implication that we prove to be sound and complete, and we then present a quadratic time closure algorithm for XFD implication. The second contribution is to investigate the implication problem for XFDs in the presence of a Document Type Definition (DTD). We show that for a class of DTDs called ‘simple’ DTDs, the implication problem for a set of XFDs and a ‘simple’ DTD can be converted to the implication problem for a set of XFDs alone, and so is axiomatizable and efficiently solvable by the first contribution. We do this by augmenting the original set of XFDs with additional XFDs generated from the structure of the DTD.