Weighted Extended Tree Transducers

The rst systematic treatment of weighted extended tree transducers (wxtt) over countably complete semirings is provided. It is proved that the extension in the left-hand sides of a wxtt can be simulated by the inverse of a linear and nondeleting tree homomorphism. In addition, a characterization of weighted tree transformations computed by bottomup wxtt in terms of bimorphisms is provided. Backward and forward application of wxtt to recognizable weighted tree languages are considered. It is shown that the backward application of a linear wxtt preserves recognizability and that the domain of an arbitrary bottom-up wxtt is recognizable. Examples demonstrate that neither backward nor forward application of arbitrary wxtt preserves recognizability. Finally, a Hasse diagram relates most of the important subclasses of weighted tree transformations computed by wxtt.