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Logic and precognizable sets of integers
 Bull. Belg. Math. Soc
, 1994
"... We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given ..."
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Cited by 68 (4 self)
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We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given by Muchnik for the theorem of CobhamSemenov, the original proof being published in Russian. 1
Cobham’s theorem for substitutions
 J. Eur. Math. Soc
"... Abstract. The seminal theorem of Cobham has given rise during the last 40 years to a lot of works around nonstandard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the socalled sub ..."
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Cited by 3 (1 self)
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Abstract. The seminal theorem of Cobham has given rise during the last 40 years to a lot of works around nonstandard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the socalled substitutive sequences. Let α and β be two multiplicatively independent Perron numbers. Then, a sequence x ∈ AN, where A is a finite alphabet, is both αsubstitutive and βsubstitutive if and only if x is ultimately periodic. 1.
Automatabased presentations of infinite structures
, 2009
"... The model theory of finite structures is intimately connected to various fields ..."
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The model theory of finite structures is intimately connected to various fields
ON THE EXPANSION (N, +, 2 x) OF PRESBURGER ARITHMETIC FRANÇOISE POINT 1
"... This is based on a preprint ([9]) which appeared in the Proceedings of the fourth ..."
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This is based on a preprint ([9]) which appeared in the Proceedings of the fourth