Two Equivalent Regularizations for Tree Adjoining Grammars

In this paper two methods of how to make derivation in a Tree Adjoining Grammar a regular process without loss of expressive power are presented and compared. In a TAG, derivation is based upon the expansion of tree nodes into other trees. One regularization method is based on an algebraic operation called Lifting, while the other exploits an additional spatial dimension by transforming the components of a TAG into three-dimensional trees. The regularized grammars generate two kinds of “encoded” trees, from which the intended ones can be reconstructed by a simple decoding function. We can show the equivalence of these methods by giving a translation between lifted and threedimensional trees and proving that via this translation it is possible to switch between the encodings without losing the information necessary for the reconstruction of the intended trees.