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Automata for arithmetic Meyer sets

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00159713
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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⟩

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