Automata for Arithmetic Meyer Sets

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


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.


Formal Addition Numeration System Algebraic Integer Admissible Representation Pisot Number 
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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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