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).

this paper we describe a statically typed XML processing language called XDuce (o#cially pronounced "transduce"). XDuce is a functional language whose primitive data structures represent XML documents and whose types---called regular expression types---correspond to document schemas. The motivating principle behind its design is that a simple, clean, and powerful type system for XML processing can be based directly on the theory of regular tree automata

... In this chapter, we shall see that the suspicion is easy dispelled. We look at techniques now used in practice for dealing with XML trees, and we note how they depart from old-fashioned uses. Since trees are objects that are very complicated to manipulate directly through pointer updates, declarative techniques are becoming increasingly important, especially when it comes to exploring, mining, and constructing tree-shaped data. In particular, we will contrast conventional concepts of database theory such as relational calculus with that of more procedural notations for trees. We explore why the essential problem of locating data in trees is intimately linked with tree automata and decidable logics, somewhat in parallel to the link between query algebras and first-order logic in relational database theory. So, we shall see why logic and automata create interesting new research opportunities.

Regular expression pattern matching is a programming language feature designed for the analysis and decomposition of XML documents.

Many useful XML transformations can be expressed by deterministic top-down tree transducers. A normal form is presented for such transducers (extended with the facility to inspect their input trees). A transducer in normal form has a unique canonical form which can be obtained by a minimization procedure, in polynomial time. Thus, equivalence of transducers in normal form can be decided in polynomial time. If the transducer is total, the normal form can be obtained in polynomial time as well. Key words: XML, top-down tree transducer, equivalence, minimization 1

ABSTRACT Many useful XML transformations can be formulated through deterministic top-down tree transducers. A canonical form for such transducers is presented which allows to decide equivalence of their induced transformations in polynomial time. If the transducer is total, the canonical form can be obtained in polynomial time as well.

Abstract Algorithms for validation and boolean operations play a crucial role in developing XML processing systems involving schemas. Although much effort has previously been made for treating elements, very few studies have paid attention to attributes. This paper presents a validation and boolean algorithms for Clark's attribute-element constraints. Although his mechanism has a prominent expressiveness and generality among other proposals, treating this is algorithmically challenging since naive approaches easily blow up even for typical inputs. To overcome this difficulty, we have developed (1) a two-phase validation algorithm that uses what we call attribute-element automata and (2) intersection and difference algorithms that proceed by a "divideand-conquer " strategy.