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) with regular look-ahead that are single use restricted. For this the single use restriction known from attribute grammars is generalized to MTTs. Since MTTs are closed under regular look-ahead, this implies that every MSO definable tree translation can be realized by an MTT. The second main result is that the class of MSO definable tree translations can also be obtained by restricting MTTs with regular look-ahead to be finite copying, i.e., to require that each input subtree is processed only a bounded number of times. The single use restriction is a rather strong, static restriction on the rules of an MTT, whereas the finite copying restriction is a more liberal, dynamic restriction on the ...

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

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...

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.

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.

Functional languages allow a modular programming style by function composition, which however can lead to inefficient runtime behavior due to production and consumption of intermediate results. We present a new mechanizable transformation technique for removing intermediate data structures in the composition of two functions from a class of recursive functions with accumulating parameters, for which classical deforestation techniques fail. In order to avoid multiple traversals of the input data structure, the composition algorithm produces circular programs that make essential use of lazy evaluation and local recursion. The resulting programs are simplified using a post-processing phase presented in the paper.

We study the problem to transform functional programs, which intensively use append functions (like inefficient list reversal), into programs, which use accumulating parameters instead (like efficient list reversal). We give an (automatic) transformation algorithm for our problem and identify a class of functional programs, namely restricted 2-modular tree transducers, to which it can be applied. Moreover, since we get macro tree transducers as transformation result and since we also give the inverse transformation algorithm, we have a new characterization for the class of functions induced by macro tree transducers.

In this paper we extend the work by Michaelis (1999) which shows how to encode an arbitrary Minimalist Grammar in the sense of Stabler (1997) into a weakly equivalent multiple contextfree grammar (MCFG). By viewing MCFG-rules as terms in a free Lawvere theory we can translate a given MCFG into a regular tree grammar. The latter is characterizable by both a tree automaton and a corresponding formula in monadic second-order (MSO) logic. The trees of the resulting regular tree language are then unpacked into the intended \linguistic" trees both through an MSO transduction based upon tree-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 characterizations of (tree) languages provide a natural framework for the denotational and opera...

Macro tree transducers can simulate most models of tree transducers (e.g., top-down and bottom-up tree transducers, attribute grammars, and pebble tree transducers which, in turn, can simulate all known models of XML transformers). The string languages generated by compositions of macro tree 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 t = (s)? It is shown that this problem can be solved (on a RAM) in time linear in the sum of the sizes of s and t. Moreover, the problem to determine, for a given t of size n, whether or not there is an input tree s such that t = (s) is in DSPACE(n); this means that output languages of compositions of macro tree transducers are deterministic context-sensitive. The involved technique of compressing intermediate results of the composition, also gives a new proof of the fact that the finiteness problem for 's range is decidable.