Formal Properties of XML Grammars and Languages

TL;DR

This paper explores the formal properties of XML grammars, showing their uniqueness, characterizations, and decidability aspects, including conditions under which they generate regular XML-languages.

Contribution

It introduces formal characterizations of XML-grammars, proves their near-uniqueness, and demonstrates decidability of certain properties specific to XML-languages.

Findings

XML-languages have essentially unique XML-grammars

Decidability of certain properties improves for XML-languages

Characterization of XML-grammars generating regular languages

Abstract

XML documents are described by a document type definition (DTD). An XML-grammar is a formal grammar that captures the syntactic features of a DTD. We investigate properties of this family of grammars. We show that every XML-language basically has a unique XML-grammar. We give two characterizations of languages generated by XML-grammars, one is set-theoretic, the other is by a kind of saturation property. We investigate decidability problems and prove that some properties that are undecidable for general context-free languages become decidable for XML-languages. We also characterize those XML-grammars that generate regular XML-languages.