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Weighted Tree Automata and Tree Transducers

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Handbook of Weighted Automata

Abstract

We survey some important results for weighted tree automata and weighted tree transducers over finite ranked trees and semirings as weight structure. In particular, we address closure properties of the class of recognizable tree series, results on the support of such tree series, the determinization of weighted tree automata, pumping lemmata and decidability results, and finite algebraic characterizations of recognizable tree series. We discuss the equivalence between recognizable tree series and equational, rational, and MSO-definable tree series, and we present a comparison of several other models of recognizability. For weighted tree transducers we show composition and decomposition results, an inclusion diagram of some fundamental classes of tree series transformations, and hierarchies obtained by composing weighted tree transducers. We also discuss other models of weighted tree transducers.

Research of the first author was supported by the Hungarian Scientific Research Fund, grant T 46686, and by the Austrian–Hungarian Action Fund, grant 68öu2.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Szeged, Árpád tér 2., 6720, Szeged, Hungary

    Zoltán Fülöp

  2. Faculty of Computer Science, Technische Universität Dresden, 01062, Dresden, Germany

    Heiko Vogler

Authors
  1. Zoltán Fülöp
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  2. Heiko Vogler
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Correspondence to Zoltán Fülöp .

Editor information

Editors and Affiliations

  1. Inst. Informatik, Universität Leipzig, Augustusplatz 10-11, Leipzig, 04109, Germany

    Manfred Droste

  2. Institut für Diskrete, TU Wien, Wiedner Hauptstr. 8-10, Wien, 1040, Austria

    Werner Kuich

  3. Fak. Informatik, TU Dresden, Nöthnitzer Str. 46, Dresden, 01187, Germany

    Heiko Vogler

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Dedicated to Symeon Bozapalidis

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Fülöp, Z., Vogler, H. (2009). Weighted Tree Automata and Tree Transducers. In: Droste, M., Kuich, W., Vogler, H. (eds) Handbook of Weighted Automata. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01492-5_9

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