Tree Adjoining G r a m m a r (TAG) is u formalism for natural language grammars. Some of the basic notions of T A G ' s were introduced in [Jo~hi,Levy, mad Takakashi I~'Sl and by [Jo~hi, l ~ l . A detailed investigation of the linguistic relevance of T A G ' s has been carried out in IKroch and Joshi,1985~. In this paper, we will describe some new results for TAG's, espe¢ially in the following areas: (I) parsing complexity of TAG's, (2) some closure results for TAG's, and (3) the relationship to Head grammars. .
