On the basis of regular tree grammars, we present a formal framework for XML schema languages. This framework helps to describe, compare, and implement such schema languages in a rigorous manner. Our main results are as follows: (1) a simple framework to study three classes of tree languages (local, single-type, and regular); (2) classification and comparison of schema languages (DTD, W3C XML Schema, and RELAX NG) based on these classes; (3) efficient document validation algorithms for these classes; and (4) other grammatical concepts and advanced validation algorithms relevant to an XML model (e.g., binarization, derivative-based validation).

A mathematical framework using formal language theory to describe and compare XML schema languages is presented. Our framework uses the work in two related areas -- regular tree languages [CDG + 97] and ambiguity in regular expressions [BEGO71, BKW98]. Using these work as well as the content in two classical references [HU79, AU79], we present the following results: (1) a normal form representation for regular tree grammars, (2) a framework of marked regular expressions and model groups, and their ambiguities, (3) five subclasses of regular tree grammars and their corresponding languages to describe XML content models: regular tree languages, TD(1) (top-down input scan with 1-vertical lookahead), single-type constraint languages, TDLL(1) (top-down and left-right input scan with 1-vertical and 1-horizontal lookaheads) , and local tree languages, (4) the closure properties of the five language classes under boolean set operations, (5) a classification and comparison of a few ...