Macro tree transducers (mtts) are a useful formal model for XML query and transformation languages. In this paper one of the fundamental decision problems on translations, namely the “translation membership problem ” is studied for mtts. For a fixed translation, the translation membership problem

Treebag is a software for experimenting with formal models in Computer Science, one type of such models being tree transducers. Tree transducers translate input trees to output trees, a mechanism used in e.g. compilers and picture generation. The top-down tree transducer is one of the formal models

Two complexity results are shown for the output languages generated by compositions of macro tree transducers. They are in NSPACE(n) and hence are context-sensitive, and the class is NP-complete.

The aim of this Dagstuhl Seminar was to bring together researchers from various research areas related to the theory and application of tree transducers. Recently, interest in tree transducers has been revived due to surprising new applications in areas such as XML databases, security verification

(represented as binary trees). On the other hand, the transformation of every mft can be simulated by the composition of two mtt's. Although macro forest transducers are more powerful, the complexity of inverse type inference, i.e., computing the pre-image of a recognizable language, is almost the same

A characterization is given of the class of tree translations definable in monadic second order logic (MSO), in terms of macro tree transducers. The first main result is that the MSO definable tree translations are exactly those tree translations realized by macro tree transducers (MTTs

transducers (obtained by reading the leaves of the output trees) form a large class which contains, e.g., the IO hierarchy and the EDT0L control hierarchy. Consider an arbitrary composition of (deterministic) macro tree transducers. How dicffiult is it, for a given input tree s, to compute the translation

-walking automata and through a macro tree transduction. This two-step approach gives an operational as well as a logical description of the tree sets involved. As an interlude we show that MCFGs can be regarded as a particularly simple attribute grammar. 1 Introduction Algebraic, logical and regular

, for a fixed output type, can be done within the same complexity as for mtts. Inverse type inference is used in algorithms for exact type checking of XML transformations. The macro tree transducer with holes (hmtt) is a new concept that is introduced in this paper. It generalizes sequence concatenation

, or XDuce. It is proved that tl, despite its expressiveness, still allows for effective inverse type inference. This result is obtained by means of a translation of tl transformers into compositions of (stay) macro tree transducers.