Abstract
Denote byDT, l-DT, andnd-HOM the class of tree transformations induced by deterministic top-down tree transducers, linear deterministic top-down tree transducers, and nondeleting homomorphism tree transducers, respectively. In this paper the classsl-DT of tree transformations induced by superlinear deterministic top-down tree transducers is considered. Some basic properties ofsl-DT are shown. Among others, it is proved thatsl-DT is not closed under composition; thatl-DT—sl-DT + ≠ O withsl-DT + being the closure ofsl-DT under composition; and thatDT = nd-HOM o sl-DT, where o denotes the operation composition of two classes. Then the hierarchy {sl-DT n n> 1} is shown to be proper, meaning thatsl-DT n ⊂sl-DT n+1, forn≥ 1. Moreover, the same is proved for the hierarchy {t-sl-DT n n ≥ 1}, wheret-sl-DT is the subclass ofsl-DT induced by total deterministic superlinear top-down tree transducers.
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