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Cut Languages in Rational Bases

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Language and Automata Theory and Applications (LATA 2017)

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

Abstract

We introduce a so-called cut language which contains the representations of numbers in a rational base that are less than a given threshold. The cut languages can be used to refine the analysis of neural net models between integer and rational weights. We prove a necessary and sufficient condition when a cut language is regular, which is based on the concept of a quasi-periodic power series. For a nonnegative base and digits, we achieve a dichotomy that a cut language is either regular or non-context-free while examples of regular and non-context-free cut languages are presented. We show that any cut language with a rational threshold is context-sensitive.

Research of both authors was done with institutional support RVO: 67985807 and partially supported by the grant of the Czech Science Foundation No. P202/12/G061.

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Authors and Affiliations

  1. Institute of Computer Science, The Czech Academy of Sciences, P.O.Box 5, 18207, Prague 8, Czech Republic

    Jiří Šíma & Petr Savický

Authors
  1. Jiří Šíma
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  2. Petr Savický
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Correspondence to Jiří Šíma .

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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Šíma, J., Savický, P. (2017). Cut Languages in Rational Bases. 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_23

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  • DOI: https://doi.org/10.1007/978-3-319-53733-7_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53732-0

  • Online ISBN: 978-3-319-53733-7

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