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. 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

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...

We investigate the typechecking problem for XML queries: statically verifying that every answer to a query conforms to a given output schema, for inputs satisfying a given input schema. As typechecking quickly turns undecidable for query languages capable of testing equality of data values, we return to the limited framework where we abstract XML documents as labeled ordered trees. We focus on simple top-down recursive transformations motivated by XSLT and structural recursion on trees. We parameterize the problem by several restrictions on the transformations (deleting, non-deleting, bounded width) and consider both tree automata and DTDs as output schemas. The complexity of the typechecking problems in this scenario range from ptime to exptime.

f on valid inputs conform to theoutput type? Since XML types are intrinsically more complex than the types found in

. Two well-known formalisms for the specication and computation of tree transductions are compared: the mso graph transducer and the attributed tree transducer with look-ahead, respectively. The mso graph transducer, restricted to trees, uses monadic second order logic to dene the output tree in terms of the input tree. The attributed tree transducer is an attribute grammar in which all attributes are trees; it is preceded by a look-ahead phase in which all attributes have nitely many values. The main result is that these formalisms are equivalent, i.e., that the attributed tree transducer with look-ahead is an appropriate implementation model for the tree transductions that are speciable in mso logic. This result holds for mso graph transducers that produce trees with shared subtrees. If no sharing is allowed, the attributed tree transducer satises the single use restriction. 1 Introduction Formulas of monadic second order (mso) logic can be used to express properti...

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.