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Laboratoire d'Informatique Algorithmique, Fondements et Applications |  |
Conference papers
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.
Cited literature [14 references]
https://hal.archives-ouvertes.fr/hal-00159713
Contributor : Christiane Frougny Connect in order to contact the contributor
Submitted on : Tuesday, May 28, 2013 - 2:35:17 PM
Last modification on : Wednesday, January 19, 2022 - 4:42:04 PM
Long-term archiving on: : Thursday, August 29, 2013 - 2:25:08 AM
Contributor : Christiane Frougny Connect in order to contact the contributor
Submitted on : Tuesday, May 28, 2013 - 2:35:17 PM
Last modification on : Wednesday, January 19, 2022 - 4:42:04 PM
Long-term archiving on: : Thursday, August 29, 2013 - 2:25:08 AM
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