This paper investigates the relationship between Context-Free Grammar (CFG) parsing and the Eisner/Satta PBDG parsing algorithms, including their extension to second-order PBDG parsing (McDonald, 2006;McDonald and Pereira, 2006).
we show how to use an off-line preprocessing step, the Unfold-Fold transformation, to transform a PBDG into an equivalent CFG that can be parsed in O(n 3 ) time using a version of the CKY algorithm with suitable indexing (Younger, 1967), and extend this transformation so that it captures second-order PBDG dependencies as well.