Automata for Arithmetic Meyer Sets
نویسندگان
چکیده
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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