Abstract. Based on the recursion mechanism of the XML transformation language XSL, the document transformation language DTL is defined. First the instantiation DTL reg is considered that uses regular expressions as pattern language. This instantiation closely resembles the navigation mechanism of XSL. For DTL reg the complexity of relevant decision problems such as termination of programs, usefulness of rules and equivalence of selection patterns, is addressed. Next, a much more powerful abstraction of XSL is considered that uses monadic second-order logic formulas as pattern language (DTL mso). If DTL mso is restricted to top-down transformations (DTL mso d), then a computational model can be defined which is a natural generalization to unranked trees of topdown tree transducers with look-ahead. The look-ahead can be realized by a straightforward bottom-up pre-processing pass through the document. The size of the output of an XSL program is at most exponential in the size of the input. By restricting copying in XSL a decidable fragment of DTL mso d programs is obtained which induces transformations of linear size increase (safe DTL mso d). It is shown that the emptiness and finiteness problems are decidable for ranges of DTL mso d programs and that the ranges are closed under intersection with generalized Document Type Definitions (DTDs). 1

Abstract. The n-pebble tree transducer was recently proposed as a model for XML query languages. The four main results on deterministic transducers are: First, (1) the translation τ of an n-pebble tree transducer can be realized by a composition of n + 1 0-pebble tree transducers. Next, the pebble tree transducer is compared with the macro tree transducer, a well-known model for syntax-directed semantics, with decidable type checking. The 0-pebble tree transducer can be simulated by the macro tree transducer, which, by the first result, implies that (2) τ can be realized by an (n+1)-fold composition of macro tree transducers. Conversely, every macro tree transducer can be simulated by a composition of 0-pebble tree transducers. Together these simulations prove that (3) the composition closure of n-pebble tree transducers equals that of macro tree transducers (and that of 0-pebble tree transducers). Similar results hold in the nondeterministic case. Finally, (4) the output languages of deterministic n-pebble tree transducers form a hierarchy with respect to the number n of pebbles. 1

. The concept of tree-based picture generation is introduced. It is shown that there are equivalent tree-based definitions of four picture-generating devices known from the literature, namely collage grammars, mutually recursive function systems, context-free chain-code grammars, and 0L-systems with turtle interpretation. Furthermore, generalisations of each of these systems are discussed. 1 Introduction During the last two decades picture generation has become a large field whose manyfold aspects are studied in mathematics as well as in practical and theoretical computer science. It attracts the interest of numerous researchers from diverse directions, which is no surprise because one can find in this area a great number of intellectually appealing mathematical and computational problems, interesting applications like the modelling of plant development and, one should not forget to mention this, an astonishing variety of beautiful pictures. In this paper picture generation is studied...

. A software system called Treebag---Tree-Based Generator---is presented. The aim behind Treebag is to allow for the generation and visualization of objects of all kinds: pictures, trees, graphs, strings, numbers, etc. The basic principle is that tree generators like, for instance, regular tree grammars, generate terms over symbols that are interpreted by appropriate algebras as operations on the domain of objects under consideration. Thus, every term is viewed as an expression that denotes one of the objects of interest. These objects can be visualized using appropriate displays. 1 Introduction In mathematics and computer science, one of the most natural and universal ways to denote elements of a given data space is to use expressions over a suitable set of operations, like p 3=7 + 5. The usefulness of this concept is even strengthened by the fact that such an expression may contain variables---in which case it does not denote a particular, single object, but a set of objects or a ...

Abstract. The first main result is that if a macro tree translation is of linear size increase, i.e., if the size of every output tree is linearly bounded by the size of the corresponding input tree, then the translation is MSO definable (i.e., definable in monadic second-order logic). This gives a new characterization of the MSO definable tree translations in terms of macro tree transducers: they are exactly the macro tree translations of linear size increase. The second main result is that given a macro tree transducer, it can be decided whether or not its translation is MSO definable, and if it is then an equivalent MSO transducer can be constructed. Similar results hold for attribute grammars, which define a subclass of the macro tree translations.

. 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

Two-way finite state transducers are considered with a fixed number of pebbles, of which the life times are nested. In the deterministic case, the transductions computed by such pebble transducers are closed under composition, and they can be realized by the composition of one-pebble transducers. The ranges of the k-pebble transducers form a hierarchy with respect to k, their finiteness problem is decidable, and they can be generated by compositions of k macro tree transducers. Re- lated results hold in the nondeterministic case.

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

A macro tree transduction is MSO definable if and only if it is of linear size increase. Furthermore, it is decidable for a macro tree transduction whether or not it is MSO definable.

Abstract. 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. 1