Compositions of n tree transducers
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Journal of Computer and System Sciences
Un théorème de duplication pour les forêts algébriques
Journal of Computer and System Sciences
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Interest in the study of sets of trees, tree languages, has led to the definition of finite automata which accept trees [2,11] and transducers which map trees into other trees [7,9,10]. These generalized machines may read treesfinite automata which accept trees [2,11] and of transducers which map trees into other trees [7,9,10]. These generalized machines may read trees either “top-down” (from the root toward the leaves) or “bottom-up” (from the leaves toward the root). Here it is shown that both the class of top-down transductions and the class of bottom-up transductions can be characterized in terms of two restricted classes of tree transductions. From these ductions and the class of bottom-up transductions can be characterized in terms of two restricted classes of tree transductions. From these characterizations, it is shown that the composition of any n bottom-up transductions can be realized by the composition of n+1 top-down transductions, and similarly, the composition of any n top-down transductions can be realized by the composition of n+1 bottom-up transductions. Next, we study the families of tree languages which can be obtained from the recognizable sets (sets accepted by finite tree automata) by the composition of n top-down or bottom-up transductions, n0. The yield operation, which concatenates the leaves of a tree from left to right to form a of string, languages from the hierarchy of families of tree languages. It is shown that each family of string languages in this hierarchy is properly contained in the family of context-sensitive languages.