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Cut Languages in Rational Bases

  • Jiří ŠímaEmail author
  • Petr Savický
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Grammars Quasi-periodic power series Cut language 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Computer ScienceThe Czech Academy of SciencesPrague 8Czech Republic

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