Automata for arithmetic Meyer sets
Résumé
The set ℤβ of β-integers is a Meyer set when β is a Pisot number, and thus there exists a finite set F such that ℤβ-ℤβ⊂ℤβ+F. We give finite automata describing the expansions of the elements of ℤβ and of ℤβ-ℤβ. 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 ℤβ-ℤβ as a sum belonging to ℤβ+F.
Domaines
Mathématique discrète [cs.DM]| Origine | Fichiers produits par l'(les) auteur(s) |
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