Systèmes de numération et automates
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Data
2002-06-30
Autores
Messaoudi, A.
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Editor
Elsevier B.V.
Resumo
Let beta be an hyperbolic algebraic integer of modulus greater than 1. Lot A be a finite set of Q[beta] and D-beta = {(a(i), b(i))(igreater than or equal to0) is an element of (A x A)(N) \ Sigma(i=0)(infinity) a(i)beta(-i)}. We give a necessary and sufficient condition for D-beta to be sofic. As a consequence, we obtain a result due to Thurston (see Corollary 1). We also treat the case where the set of digits A is given by the greedy algorithm and study the connection with the beta-shift. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
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Comptes Rendus Mathematique. Paris Cedex 15: Editions Scientifiques Medicales Elsevier, v. 334, n. 12, p. 1043-1046, 2002.