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Superlinear deterministic top-down tree transducers

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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 + ≠ Ø 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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Authors and Affiliations

  1. Department of Foundations of Computer Science, József Attila University, Aradi Vértanúk tere 1, H-6720, Szeged, Hungary

    G. Dányi

  2. Department of Computer Science, József Attila University, Árpád tér 2, H-6720, Szeged, Hungary

    Z. Fülöp

Authors
  1. G. Dányi
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  2. Z. Fülöp
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Additional information

The research of the first author was supported by Grant FOI 12852 of the Research Foundation of Hungary, and that of the second author was supported by Grant 2035 of the Research Foundation of Hungary.

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Dányi, G., Fülöp, Z. Superlinear deterministic top-down tree transducers. Math. Systems Theory 29, 507–534 (1996). https://doi.org/10.1007/BF01184813

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  • DOI: https://doi.org/10.1007/BF01184813

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