Two Equivalent Regularizations for Tree Adjoining Grammars

Authors:
Anna Kasprzik
Affiliations:
Informatik FB IV, University of Trier, Trier, D-54286
Venue:
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Year:
2009

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Abstract

We present and compare two methods of how to make derivation in a Tree Adjoining Grammar a regular process (in the Chomsky hierarchy sense) without loss of expressive power. 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 two two-step approaches by giving a direct translation between lifted and three-dimensional 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.