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

Authors:
Andreas Maletti;Cătălin Ionuţ Tîrnăucă
Affiliations:
Departament de Filologies Romàniques, Universitat Rovira i Virgili, Tarragona, Spain 43002;Departament de Filologies Romàniques, Universitat Rovira i Virgili, Tarragona, Spain 43002
Venue:
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
Year:
2009

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Abstract

Quasi-alphabetic tree bimorphisms [Steinby , Tîrnă ucă : Defining syntax-directed translations by tree bimorphisms. Theor. Comput. Sci. , to appear. http://dx.doi.org/10.1016/j.tcs.2009.03.009 , 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.