Expressiveness of Structured Document Query Languages Based on Attribute Grammars

Abstract

Structured document databases can be naturally viewed as derivation trees of a context-free grammar. Under this view, the classical formalism of attribute grammars becomes a formalism for structured document query languages. From this perspective, we study the expressive power of BAGs: Boolean-valued attribute grammars with propositional logic formulas as semantic rules, and RAGs: relation-valued attribute grammars with first-order logic formulas as semantic rules. BAGs can express only unary queries; RAGs can express queries of any arity. We first show that the (unary) queries expressible by BAGs are precisely those definable in monadic second-order logic. We then show that the queries expressible by RAGs are precisely those definable by first-order inductions of linear depth, or, equivalently, those computable in linear time on a parallel machine with polynomially many processors. We finally show that RAGs are more powerful than monadic second-order logic for queries of any arity.