Automata for arithmetic Meyer sets

Shigeki Akiyama (1) , Frédérique Bassino (2) , Christiane Frougny (3)

1 Department of Mathematics
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
3 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

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.

Domaines: Mathématique discrète [cs.DM]

Shigeki Akiyama, Frédérique Bassino, Christiane Frougny. Automata for arithmetic Meyer sets. LATIN 04, 2004, Buenos-Aires, Argentina. pp.252-261, ⟨10.1007/978-3-540-24698-5_29⟩. ⟨hal-00159713⟩