Extensions of Attribute Grammars for Structured Document Queries

Widely-used document speciication languages like, e.g., SGML and XML, model documents using extended context-free grammars. These diier from standard context-free grammars in that they allow arbitrary regular expressions on the right-hand side of productions. To query such documents, we introduce a new form of attribute grammars (extended AGs) that work directly over extended context-free grammars rather than over standard context-free grammars. Viewed as a query language, extended AGs are particularly relevant as they can take into account the inherent order of the children of a node in a document. We show that two key properties of standard attribute grammars carry over to extended AGs: eeciency of evaluation and decidability of well-deenedness. We further characterize the expressiveness of extended AGs in terms of monadic second-order logic, establish the complexity of their non-emptiness and equivalence problem to be complete for EXPTIME, and consider several extensions of extended AGs. As an application we show that the Region Algebra expressions introduced by Consens and Milo can be eeciently translated into extended AGs. This translation drastically improves the known upper bound on the complexity of the emptiness and equivalence test for Region Algebra expressions.