The connection between Context-free grammars and XML

Guðmundur Freyr Jónasson

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Context-Free Grammars

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Variables: A, BTerminals: 0, 1, #Nr of rules: 3

Derivation of the string 000#111:

Document Type Definition (DTD)

• DTD defines the legal building blocks of an XML document with a list of legal elements and attributes.

• XML validity requires that a document follows the constraints expressed in its document type definition, which provides a rough equivalence to a context-free grammar for a document type.

• DTD is specified using “Extended Context-Free Grammar”.

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Extended Context-Free Grammar• Allows regular expressions over terminals and non-terminals on the

right hand side of productions.

• The regular expression operators are , * and concatenation.∪

• We could write grammar G as follows:

Or

Where S is the start symbol in both cases.

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DTD Syntax

• < !ELEMENT name (model) >– ELEMENT is a keyword– name is the the element name being declared– model is the elements content model

• The content model is specified using a regular expression over element names.

• We now have sequences of element names rather then sequences of symbols (strings) like in CFG.

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Regular Expressions vs. DTD Syntax

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CFG and DTD example

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Conclusion

• Both DTD for XML and CFG describe languages with certain rules and restrictions, and thereby declare what’s legal and what’s not in a given language.

• An XML document is considered valid if it’s well formed and has been validated against a DTD.

• A string is a valid string in a given Context-free language if the Context-free grammar for that language can generate it.

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References• Introduction to the Theory of Computation, 2nd edition, M. Sipser, Course

Technology, 2005.

• W3Schools – Learn DTD: http://w3schools.com/dtd/default.asp

• Extensible Markup Language (XML) Fourth Edition: http://www.w3.org/TR/REC-xml/

• Languages, Grammars and DTDs: http://www.dcs.bbk.ac.uk/~ptw/teaching/dtd-new/notes.html

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