Theory of Computing Systems

, Volume 60, Issue 2, pp 129–171 | Cite as

Composition Closure of Linear Extended Top-down Tree Transducers

  • Joost Engelfriet
  • Zoltán Fülöp
  • Andreas MalettiEmail author


Linear extended top-down tree transducers (or synchronous tree-substitution grammars) are popular formal models of tree transformations that are extensively used in syntax-based statistical machine translation. The expressive power of compositions of such transducers with and without regular look-ahead is investigated. In particular, the restrictions of ε-freeness, strictness, and nondeletion are considered. The composition hierarchy turns out to be finite for all ε-free (all rules consume input) variants of these transducers except for the nondeleting ε-free transducers. The least number of transducers needed for the full expressive power of arbitrary compositions is presented. In all remaining cases (incl. the nondeleting ε-free transducers) the composition hierarchy does not collapse.


Extended top-down tree transducer Composition hierarchy Bimorphism 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Leiden Institute of Advanced Computer ScienceLeiden UniversityLeidenThe Netherlands
  2. 2.Department of Foundations of Computer ScienceUniversity of SzegedSzegedHungary
  3. 3.Institute of Computer ScienceUniversität LeipzigLeipzigGermany

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