Fourth normal form and free redundancy for XML document based on path expression

With extensible Markup Language (XML) becoming more and more popular, to avoid the redundancy, XML schema design has become an important issue. So the normalization of XML is a hotspot in research field. Similar to relational database, this paper is database based with the goal of eliminating the data redundancy, to study the concepts of path expression in Document Type Definition(DTD). In this paper, XML is extended with functional dependency(XFD) and multi-valued dependency(XMVD), which are fundamental to semantic specification. And make formalized definitions on XFD and XMVD; Based on the concepts of XML tree and data dependency, it provides the description of key and redundancy. On the condition of the coexistence of XFD and XMVD, it further proposes the terms to meet the fourth normal form(4XNF) and provides theorem to determine the XML document tree which meets the above terms without redundancy, and the sound of the 4XNF is proved by experiment.