Linear Time Membership for a Class of XML Types with Interleaving and Counting

Regular Expressions (REs) form the basis of most XML type languages, such as DTDs, XML Schema types, and XDuce types (Thompson et al. 2004; Hosoya and Pierce 2003). In this context, the interleaving operator would be a natural addition to the language of REs, as witnessed by the presence of limited forms of interleaving in XSD (the all group), Relax-NG, and SGML. Unfortunately, membership checking for REs with interleaving is NP-hard in general. We present here a restricted class of REs with interleaving and counting which admits a linear membership algorithm. This restricted class is known to be expressive enough for the vast majority of the content models used in real-world DTDs and XSD schemas; moreover, we have proved in (Ghelli et al. 2007) that the same class admits a polynomial algorithm for subtyping and typeequivalence, problems which are EXPSPACE-complete for the full language of REs with interleaving. We first present an algorithm for membership of a list of words into a RE with interleaving and counting, based on the translation of the RE into a set of constraints. We generalize the approach in order to check membership of XML trees into a class of EDTDs with interleaving and counting, which models the crucial aspects of DTDs and XSD schemas. Finally, we extend the approach to REs with intersection.