. Attributed tree transducers are formal models for studying properties of attribute grammars. In this paper we prove a two--dimensional hierarchy for classes of producing attributed tree transducers. The two dimensions refer to the maximum number of synthesized and inherited attributes, respectively. To this end we apply a pumping lemma for output languages of producing attributed tree transducers. 1 Introduction The concept of attributed tree transducer (in the following abbreviated by att) has been invented by Fulop in [6] (cf. also [4]). Atts are abstractions of attribute grammars, which were introduced by Knuth in [9] in order to describe the semantics and the translation of programming languages. An att takes a tree over a ranked alphabet of input symbols rather than a derivation tree as argument. The attribute values are also trees over a ranked alphabet of output symbols. Attribute grammars and atts are related to the concept of attributed tree grammar which was introduced in ...

. The class of string languages obtained by taking the yields of output tree languages of total deterministic macro tree transducers (MTTs) is investigated. The first main result is that MTTs which are linear and nondeleting in the parameters generate the same class of string languages as total deterministic top-down tree transducers. The second main result is a so called "bridge theorem"; it can be used to show that there is a string language generated by a nondeterministic top-down tree transducer with monadic input, i.e., an ET0L language, which cannot be generated by an MTT. In fact, it is shown that this language cannot even be generated by the composition closure of MTTs; hence it is also not in the IO-hierarchy. 1

This first chapter gives an introduction into the area of tree transducer theory, and describes the results presented in Chapters 2–6. The first section addresses general issues like translations, trees, and tree grammars. Section 2 is concerned with the different models of tree transducers that are considered in the thesis. It describes the typical problems that appear in tree transducer theory, and mentions important properties of the different tree transducer models. Section 3 describes the results of

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Math. Rainer Vater Tel.: (+49) 351 - 463 8487 E-mail: Rainer.Vater@inf.tu-dresden.de Annual Report 2000 3 Ph.D. students of the DFG (German Research Foundation): Dipl.-Math. Claus Jurgensen (from May 1st) Tel.: (+49) 351 - 463 8253 E-mail: claus@orchid.inf.tu-dresden.de Scientic Auxiliaries: Dipl.-Inf. Enrico Bormann (from May 16th) Tel.: (+49) 351 - 463 8374 E-mail: Enrico.Bormann@inf.tu-dresden.de Student Auxiliaries: Sean Eikenberg (until January 31st) Ivonne Frank (from October 16th) Andreas Maletti (from October 16th) Alexander Motzkau (until July 31st and from October 1st) Michael Peter (from February 1st until March 31st) Janis Voigtlander (from April 1st until September 30th) Foundations of Programming 3 Teaching 3.1 Teaching Areas in general Compiler construction