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Section: Scientific Foundations

Keywords : semi-structured documents, trees, queries, transformations, automata, logic.

Modeling XML document transformations

XML document transformations can be defined in W3C standards languages XQuery or XSLT . Programming XML transformations in these languages is often difficult and error prone even if the schemata of input and output documents are known. Advanced programming experience and considerable programming time may be necessary, that are not available in Web services or similar scenarios.

Alternatives programming language for defining XML transformations have been proposed by the programming language community, for instance XDuce [41] , Xtatic [39] , [44] , and CDuce [28] , [29] , [31] . The type systems of these languages simplify the programming tasks considerably. But of course, they don't solve the general difficulty in programming XML transformations manually.

Languages for defining node selection queries arise as sub-language of all XML transformation languages. The W3C standards use XPath for defining monadic queries, while XDuce and CDuce rely on regular queries defined by regular pattern equivalent to tree automata. Indeed, it is natural to look at node selection as a simple form of tree transformation. Monadic node selection queries correspond to deterministic transformations that annotate all selected nodes positively and all others negatively. N-ary node selection queries become non-deterministic transformations, yielding trees annotated by Boolean vectors.

After extensive studies of node selection queries in trees (in XPath or many other languages) the XML community has started more recently to formally investigate XML tree transformations. The expressiveness and complexity of XQuery are studied in [43] , [53] . Type preservation is another problem, i.e., whether all trees of the input type get transformed into the output type, or vice versa, whether the inverse image of the output type is contained in the input type [47] , [45] .

The automata community usually approaches tree transformations by tree transducers [37] , i.e., tree automata producing output structure. Macro tree transducers, for instance, have been proposed recently for defining XML transformations [45] , [48] . From the view point of logics, tree transducers have been studied for MSO definability [38] .


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