Multi-dimensional Trees and a Chomsky-Schützenberger-Weir Representation Theorem for Simple Context-Free Tree Grammars

摘要

David J. Weir proved a Chomsky-Schützenberger-like representation theorem for the string languages of tree-adjoining grammars. This paper presents a generalization of this theorem to the string languages of simple (i.e., linear and non-deleting) context-free tree grammars. This result is obtained through a natural generalization of the original Chomsky-Schützenberger theorem to the tree languages of simple context-free tree grammars. We use James Rogers's notion of multi-dimensional trees to state this latter theorem in a very general, abstract form.