The Sufficient and Necessary Condition for No Implicit Redundancies in an XML Schema

XML has emerged as a standard for data representation and interchange on the Internet. Normally the first step for building an XML application is XML database schema design. Normalization design of XML database schema is generating a set of related XML schemas or DTDs that can represent data dependencies and eliminate redundancies, in order to make information retrieval better. The reason why redundancies exist in an XML database schema is that there exist some data dependencies in it. So relationship between data dependencies and redundancies in an XML database schema is a key problem for researches on its normalization design. But there is no research on it now. Data dependencies in an XML database schema consist of data dependencies among attributes and among elements. Data dependencies in an XML database schema by synthesizing data dependencies among attributes and among elements are defined, implicit redundancies relating to it are analyzed, and semi-normal XML schema and normal XML schema are defined based on it. Then the sufficient and necessary condition that no implicit redundancies exist in an XML schema iff the XML schema is normal is proved. This work lays a theoretical foundation for the further research on normalization design of XML database schema.