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Sequentiality of Group-Weighted Tree Automata

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Language and Automata Theory and Applications (LATA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12638))

Abstract

We introduce the notion of group-weighted tree automata over commutative groups and characterise sequentialisability of such automata. In particular, we introduce a fitting notion for tree distance and prove the equivalence between sequentialisability, the so-called Lipschitz property, and the so-called twinning property.

Research of the first and third author was supported by the DFG through the Research Training Group QuantLA (GRK 1763). The second author was supported by the European Research Council (ERC) through the ERC Consolidator Grant No. 771779 (DeciGUT).

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Notes

  1. 1.

    A loop is a run on a context tree such that the state at the context variable is the same as the state at the root of the context.

  2. 2.

    In fact, we do not require commutativity for the proof our results. However, in order to limit the notational complexity of the present paper, we require \(\mathbb {G}\) to be commutative.

  3. 3.

    As a reference, we use the definition of semiring-weighted tree automata from [5]. For a more thorough introduction to semirings confer [12] and for semiring-\(\mathrm {WTA}\) we refer to [11].

  4. 4.

    That is, a tuple satisfying the conditions of a \(\mathrm {WTA}\), except for finiteness.

  5. 5.

    Formally, we have a globally fixed choice function and then simply define .

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Author information

Authors and Affiliations

  1. Faculty of Computer Science, Technische Universität Dresden, Dresden, Germany

    Frederic Dörband & Thomas Feller

  2. Institute of Computer Science, Universität Leipzig, Leipzig, Germany

    Kevin Stier

Authors
  1. Frederic Dörband
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  2. Thomas Feller
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  3. Kevin Stier
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Corresponding author

Correspondence to Frederic Dörband .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Alberto Leporati

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. Ariel University, Ariel, Israel

    Dana Shapira

  4. University of Milano-Bicocca, Milan, Italy

    Claudio Zandron

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Dörband, F., Feller, T., Stier, K. (2021). Sequentiality of Group-Weighted Tree Automata. In: Leporati, A., Martín-Vide, C., Shapira, D., Zandron, C. (eds) Language and Automata Theory and Applications. LATA 2021. Lecture Notes in Computer Science(), vol 12638. Springer, Cham. https://doi.org/10.1007/978-3-030-68195-1_21

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  • DOI: https://doi.org/10.1007/978-3-030-68195-1_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-68194-4

  • Online ISBN: 978-3-030-68195-1

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