Output String Languages of Compositions of Deterministic Macro Tree Transducers

Abstract

The composition of total deterministic macro tree transducers gives rise to a proper hierarchy with respect to their output string languages (these are the languages obtained by taking the yields of the output trees). There is a language not in this hierarchy which can be generated by a (quite restricted) nondeterministic string transducer, namely, a two-way generalized sequential machine. Similar results hold for attributed tree transducers, for controlled EDT0L systems, and for YIELD mappings (which proves properness of the IO-hierarchy). Witnesses for the properness of the macro tree transducer hierarchy can already be found in the latter three hierarchies. © 2002 Elsevier Science (USA)

Sound, fine-grained traversal fusion for heterogeneous trees

“…Figure 12 shows the performance of fused traversals corresponding to the first equation in Table 6 for different depths of kd-tree, normalized to the unfused ones. 10 The fused traversals reduce node visits by 83%, and we see a 90% reduction in L2 cache misses. Overall, the fused traversals are faster, with a runtime improvement ranging from 15% for small trees, to 66% for large ones.…”

“…Another specialized way to express tree traversals is by using attribute grammars to specify tree transducers-automata that traverse trees and create output [6,9]. Using this specialized representation of programs, subsequent authors were able to improve efficiency of compositions of tree transducers [10,18]. However, to our knowledge none of these approaches handle as general a class of programs and fusion opportunities as Grafter: for example, we are not aware of a tree transducer solution for partial fusion.…”

Equivalence of Deterministic Top-Down Tree-to-String Transducers is Decidable

“…For the specific sub-class of linear yDT transducers, we obtain an algorithm with by far better complexity bounds as those provided by the construction in [34]. General MSO definable tree-to-string transductions on the other hand, can be simulated by yDT transducers with regular look-ahead (see [45], [46]). Since equivalence of yDT transducers with regular look-ahead can be reduced to equivalence of yDT transducers without look-ahead but relative to a DTTA automaton, our decidability result encompasses the decidability result for MSO definable tree-to-string transductions.…”

A Survey on Decidable Equivalence Problems for Tree Transducers

“…The idea is to provide multiple parameters, whenever parameters are copied, and to use regular look-ahead in order to determine which parameters are deleted. For a ymtt R transducer that is special in the parameters, it is shown in Lemma 13 of [29] how to construct an equivalent yt R transducer. The parameters of the ymtt can be removed by outputting the strings between them directly.…”

“…Top-down tree transducers generalize to trees the finite state (string) transducers (also known as "generalized sequential machines", or gsms, see [47,9]). In terms of formal languages, compositions of mtts give rise to a large hierarchy of string languages containing, e.g., the io and oi hierarchies of Damm [23] (at level one they include the indexed languages of Aho [1]), see also [29]. The latter hierarchies can be obtained by restricting higher-order recursive program schemes Macro tree transducers can be applied in many scenarios, recently for instance, to type-check xml transformations (they can simulate the k-pebble transducers of Milo, Suciu, and Vianu [64]), see [30,61,62], or to efficiently implement streaming XQuery transformations [51,65].…”