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Schema validators work by using the schema to build an internal
representation of the grammar described in the schema. Typically, a state
machine is created from the grammer and then the document is tested against
the state machine.
One way to think of it is that it is a bit like a generalized programming
language. Programming languages are typically described formally by
grammars. Tools such as YACC allow programmers to describe grammers and
then generate code to validate programs against the grammar. An XML
validator is a bit like that except that the YACC part of the process
happens "on the fly".
The best place to look if you are interested in XML validators is the
branch of computer science that deals with parsing. The classic text is the
"dragon book" by Aho and Ullman
(http://www.jargon.net/jargonfile/d/DragonBook.html).
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