Extended top-down tree transducers (transducteurs generalises descendants [Arnold, Dauchet: Bi-transductions de forets. ICALP'76. Edinburgh University Press. 1976]) received renewed interest in the field of Natural Language Processing. Here those transducers are extensively and systematically studied. Their main properties are identified and their relation to classical top-down tree transducers is exactly characterized. The obtained properties completely explain the Hasse diagram of the induced classes of tree transformations. In addition, it is shown that most interesting classes of transformations computed by extended top-down tree transducers are not closed under composition.

We study automata for capturing transformations employed by practical natural language processing systems, such as those that translate between human languages. For several variations of finite-state string and tree transducers, we ask formal questions about expressiveness, modularity, teachability, and generalization.

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Synchronous tree substitution grammars are a translation model that is used in syntax-based machine translation. They are investigated in a formal setting and compared to a competitor that is at least as expressive. The competitor is the extended multi bottom-up tree transducer, which is the bottom-up analogue with one essential additional feature. This model has been investigated in theoretical computer science, but seems widely unknown in natural language processing. The two models are compared with respect to standard algorithms (binarization, regular restriction, composition, application). Particular attention is paid to the complexity of the algorithms. 1

Abstract. Extended multi bottom-up tree transducers are de ned and investigated. They are an extension of multi bottom-up tree transducers by arbitrary, not just shallow, left-hand sides of rules; this includes rules that do not consume input. It is shown that such transducers can compute any transformation that is computed by a linear extended top-down tree transducer. Moreover, the classical composition results for bottomup tree transducers are generalized to extended multi bottom-up tree transducers. Finally, a characterization in terms of extended top-down tree transducers is presented. 1

Weighted tree transducers have been proposed as useful formal models for representing syntactic natural language processing applications, but there has been little description of inference algorithms for these automata beyond formal foundations. We give a detailed description of algorithms for application of cascades of weighted tree transducers to weighted tree acceptors, connecting formal theory with actual practice. Additionally, we present novel on-the-fly variants of these algorithms, and compare their performance on a syntax machine translation cascade based on (Yamada and Knight, 2001). 1

Abstract. Top-down tree transducers with "-rules ("tdtt) are a restricted version of extended top-down tree transducers. They are implemented in the framework Tiburon and ful ll some criteria desirable in a machine translation model. However, they compute a class of transformations that is not closed under composition (not even for linear and nondeleting "tdtt). A composition construction that composes "tdtt M and N is presented. It is correct whenever (i) M has at most one output symbol in each rule, (ii) M is deterministic or N is linear, and (iii) M is total or N is nondeleting. This corresponds nicely to a classical composition result by Baker. 1

Synchronous tree insertion grammars (STIG) are formal models for syntaxbased machine translation. We formalize a decoder for probabilistic STIG; the decoder transforms every source-language string into a target-language tree and calculates the probability of this transformation. 1

In this survey, several model of tree transducers are investigated with respect to properties that are relevant in machine translation. These properties include: suitable expressiveness, symmetry, preservation of regularity, and closure under composition. For three tree transducer models, top-down tree transducers, extended top-down tree transducers, and extended multi bottom-up tree transducers, the relevant results are presented in an informal and illustrative manner. The aim of the survey is provide a synopsis that illustrates how theory (tree transducers) and practice (machine translation) interact on this particular example. Additional details can be found in the original results that are referenced throughout the text.

The first systematic treatment of weighted extended tree transducers (wxtt) over countably complete semirings is provided. It is proved that the extension in the left-hand sides of a wxtt can be simulated by the inverse of a linear and nondeleting tree homomorphism. In addition, a characterization of weighted tree transformations computed by bottom up wxtt in terms of bimorphisms is provided. Backward and forward application of wxtt to recognizable weighted tree languages are considered. It is shown that the backward application of a linear wxtt preserves recognizability and that the domain of an arbitrary bottom-up wxtt is recognizable. Examples demonstrate that neither backward nor forward application of arbitrary wxtt preserves recognizability. Finally, a Hasse diagram relates most of the important subclasses of weighted tree transformations computed by wxtt.