On the Generating Power of Deterministic Tree Transducers

Attributed tree transducers are abstract models 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. generating power. We give two applications of our results: (1) there is no attributed tree transducer which computes the set of all monadic trees with exponential height as output language and (2) there is a hierarchy of output languages of attributed tree transducers w.r.t. their number of attributes. The latter result is achieved by proving a hierarchy of tree languages generated by context{free hypergraph grammars w.r.t. their rank.