Which XML Schemas Admit 1-Pass Preorder Typing?

It is shown that the class of regular tree languages admitting one-pass preorder typing is exactly the class defined by restrained competition tree grammars introduced by Murata et al. [14]. In a streaming context, the former is the largest class of XSDs where every element in a document can be typed when its opening tag is met. The main technical machinery consists of semantical characterizations of restrained competition grammars and their subclasses. In particular, they can be characterized in terms of the context of nodes, closure properties, allowed patterns and guarded DTDs. It is further shown that deciding whether a schema is restrained competition is tractable. Deciding whether a schema is equivalent to a restrained competition tree grammar, or one of its subclasses, is much more difficult: it is complete for EXPTIME. We show that our semantical characterizations allow for easy optimization and minimization algorithms. Finally, we relate the notion of one-pass preorder typing to the existing XML Schema standard.

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