Attribute grammars for unranked trees as a query language for structured documents

Abstract

Document specification languages, like for instance XML, model documents using extended context-free grammars. These differ from standard context-free grammars in that they allow arbitrary regular expressions on the fight-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 non-circularity remains decidable in EXPTIME and establish the complexity of the non-emptiness and equivalence problem of extended AGs to be complete for EXPTIME. As an application we show that the Region Algebra expressions can be efficiently 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 from non-elementary to EXPTIME. Finally, we characterize the expressiveness of extended AGs in terms of monadic second-order logic.