Syntax-Directed Translations and Quasi-alphabetic Tree Bimorphisms — Revisited

  • Andreas Maletti
  • Cătălin Ionuţ Tîrnăucă
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5725)


Quasi-alphabetic tree bimorphisms [Steinby, Tîrnă ucă: Defining syntax-directed translations by tree bimorphisms. Theor. Comput. Sci., to appear. , 2009] are reconsidered. It is known that the class of (string) translations defined by such bimorphisms coincides with the class of syntax-directed translations. This result is extended to a smaller class of tree bimorphisms namely (linear and complete) symbol-to-symbol tree bimorphisms. Moreover, it is shown that the class of simple syntax-directed translations coincides with the class of translations defined by alphabetic tree bimorphisms (also known as finite-state relabelings). This proves that alphabetic tree bimorphisms are not sufficiently powerful to model all syntax-directed translations. Finally, it is shown that the class of tree transformations defined by quasi-alphabetic tree bimorphisms is closed under composition. The corresponding result is known in the variable-free case. Overall, the main results of [Steinby, Tîrnă ucă] are strengthened.


syntax-directed translation regular tree language tree bimorphism natural language processing 


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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Andreas Maletti
    • 1
  • Cătălin Ionuţ Tîrnăucă
    • 1
  1. 1.Departament de Filologies RomàniquesUniversitat Rovira i VirgiliTarragonaSpain

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