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International Conference on Language and Automata Theory and Applications

LATA 2017: Language and Automata Theory and Applications pp 405–417Cite as

On the Computational Power of Affine Automata

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10168)

Abstract

We investigate the computational power of affine automata (AfAs) introduced in [4]. In particular, we present a simpler proof for how to change the cutpoint for any affine language and a method how to reduce error in bounded error case. Moreover, we address to the question of [4] by showing that any affine language can be recognized by an AfA with certain limitation on the entries of affine states and transition matrices. Lastly, we present the first languages shown to be not recognized by AfAs with bounded-error.

Keywords

  • Non-classical models of automata
  • Affine automata
  • Cutpoint languages
  • Bounded error
  • Compact sets
  • Error reduction

M. Hirvensalo—Partially supported by Väisälä Foundation.

E. Moutot—Partially supported by TUCS COM\({}^3\)-project and ANR project CoCoGro (ANR-16-CE40-0005).

A. Yakaryılmaz—Partially supported by TUCS COM\({}^3\)-project and ERC Advanced Grant MQC.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Turku, 20014, Turku, Finland

    Mika Hirvensalo

  2. LIP, ENS de Lyon – CNRS – INRIA – UCBL – Université de Lyon, École Normale Supérieure de Lyon, 69007, Lyon, France

    Etienne Moutot

  3. Faculty of Computing, University of Latvia, Raina Bulv. 19, Riga, 1586, Latvia

    Abuzer Yakaryılmaz

  4. Turku Centre for Computer Science (TUCS), Turku, Finland

    Mika Hirvensalo

Authors
  1. Mika Hirvensalo
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  2. Etienne Moutot
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  3. Abuzer Yakaryılmaz
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Corresponding authors

Correspondence to Mika Hirvensalo , Etienne Moutot or Abuzer Yakaryılmaz .

Editor information

Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Frank Drewes

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. University of Giessen, Giessen, Germany

    Bianca Truthe

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Hirvensalo, M., Moutot, E., Yakaryılmaz, A. (2017). On the Computational Power of Affine Automata. In: Drewes, F., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2017. Lecture Notes in Computer Science(), vol 10168. Springer, Cham. https://doi.org/10.1007/978-3-319-53733-7_30

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  • DOI: https://doi.org/10.1007/978-3-319-53733-7_30

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