The Generating Power of Total Deterministic Tree Transducers

Attributed tree transducers are abstract models used to study properties of attribute grammars. One abstraction which occurs when modeling attribute grammars by attributed tree transducers is that arbitrary trees over a ranked alphabet are taken as input, instead of derivation trees of a context-free grammar. In this paper we show that with respect to the generating power this is not an abstraction; i.e., we show that attributed tree transducers and attribute grammars generate the same class of term (or tree) languages. To prove this, a number of results concerning the generating power of top-down tree transducers are established, which are interesting in their own. We also show that the classes of output languages of attributed tree transducers form a hierarchy with respect to the number of attributes. The latter result is achieved by proving a hierarchy of classes of tree languages generated by context-free hypergraph grammars with respect to their rank. ] 1998 Academic Press