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The Complexity of Compositions of Deterministic Tree Transducers

  • Sebastian Maneth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2556)

Abstract

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 τ of (deterministic) macro tree transducers. How dificult is it, for a given input tree s, to compute the translation t = τ (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 = τ (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 τ ’s range is decidable.

Keywords

Deterministic Macro Tree Transducers Complexity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Sebastian Maneth
    • 1
  1. 1.LIACSLeiden UniversityRA LeidenThe Netherlands

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