Many probabilistic models for natural language are now written in terms of hierarchical tree structure. Tree-based modeling still lacks many of the standard tools taken for granted in (finite-state) string-based modeling. The theory of tree transducer automata provides a possible framework to draw on, as it has been worked out in an extensive literature. We motivate the use of tree transducers for natural language and address the training problem for probabilistic tree-totree and tree-to-string transducers.

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

We present a technique to prevent the construction of intermediate data structures in functional programs, which is based on results from the theory of tree transducers. We first decompose function definitions, which correspond to macro tree transducers, into smaller pieces. Under certain restrictions...

We generalize bottom-up tree transducers and top-down tree transducers to the concept of bottom-up tree series transducer and top-down tree series transducer, respectively, by allowing formal tree series as output rather than trees, where a formal tree series is a mapping from output trees to some semiring. We associate two semantics with a tree series transducer: a mapping which transforms trees into tree series (for short: tree to tree series transformation or t-ts transformation), and a mapping which transforms tree series into tree series (for short: tree series transformation or ts-ts transformation). We show that the standard case of tree transducers is reobtained by choosing the boolean semiring under the t-ts semantics. Also, for each of the two types of tree series transducers and for both types of semantics, we prove a characterization which generalizes in a straightforward way the corresponding characterization result for the underlying tree transducer class. Mo...

Many functional programs with accumulating parameters are contained in the class of macro tree transducers. We present a program transformation technique that can be used to solve the efficiency problems due to creation and consumption of intermediate data structures in compositions of such functions, where classical deforestation techniques fail. In order to do so, given two macro tree transducers under appropriate restrictions, we construct a single macro tree transducer that implements the composition of the two original ones. The imposed restrictions are more liberal than those in the literature on macro tree transducer composition, thus generalising previous results.

We compare transformations for the elimination of intermediate results in first-order functional programs. We choose the well known deforestation technique of Wadler and composition techniques from the theory of tree transducers, of which the implementation of functional programs yet does not take advantage. We identify syntactic classes of function definitions for which both techniques deliver equally efficient results and for which one technique is more powerful than the other.

In this paper we prove Kleene's result for tree series over a commutative and idempotent semiring A (which is not necessarily complete or continuous), i.e., the class of recognizable tree series over A and the class of rational tree series over A are equal. We show the result by direct automata-theoretic constructions and prove their correctness.

. The finiteness of ranges of tree transductions is shown to be decidable for TBY + , the composition closure of macro tree transductions. Furthermore, TBY + definable sets and TBY + computable relations are considered, which are obtained by viewing a tree as an expression that denotes an element of a given algebra. A sufficient condition on the considered algebra is formulated under which the finiteness problem is decidable for TBY + definable sets and for the ranges of TBY + computable relations. The obtained result applies in particular to the class of string languages that can be defined by TBY + transductions via the yield mapping. This is a large class which is proved to form a substitution-closed full AFL. 1 Introduction The finiteness problem is one of the classical decidability problems in formal language theory. For a given language of interest, one usually does not wish to know whether that language is finite (because it usually is not), but rather whether the l...

. 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...

We investigate the determinization of nondeterministic bottom-up/top-down finite state weighted tree automata over some semiring A and compare the resulting four classes of formal tree series with each other. In fact, we generalize well known theorems on classes of tree languages (cf. [GS84] Chapter II, Theorems 2.6 and 2.10, Example 2.11), viz. if A is a commutative and locally finite semifield, then (i) nondeterministic bottom-up, (ii) deterministic bottom-up, and (iii) nondeterministic top-down finite state weighted tree automata are equally powerful. Moreover, if the input alphabet is not trivial, then deterministic top-down finite state weighted tree automata are strictly less powerful than the aforementioned classes.