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Automata for Arithmetic Meyer Sets

  • Shigeki Akiyama
  • Frédérique Bassino
  • Christiane Frougny
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2976)

Abstract

The set ℤ β of β-integers is a Meyer set when β is a Pisot number, and thus there exists a finite set F such that ℤ β  − ℤ β  ⊂ ℤ β  + F. We give finite automata describing the expansions of the elements of ℤ β and of ℤ β  − ℤ β . We present a construction of such a finite set F, and a method to minimize the size of F. We obtain in this way a finite transducer that performs the decomposition of the elements of ℤ β  − ℤ β as a sum belonging to ℤ β  + F.

Keywords

Formal Addition Numeration System Algebraic Integer Admissible Representation Pisot Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Shigeki Akiyama
    • 1
  • Frédérique Bassino
    • 2
  • Christiane Frougny
    • 3
  1. 1.Department of Mathematics, Faculty of SciencesNiigata UniversityNiigataJapan
  2. 2.Institut Gaspard MongeUniversité de Marne-la-ValléeMarne-la-Vallée Cedex 2France
  3. 3.LIAFA, UMR 7089, and Université Paris 8Paris Cedex 05France

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