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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 70 (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
A generalization of Cobham’s theorem
 Theory Comput. Syst
, 1998
"... Abstract If a nonperiodic sequence X is the image by a morphism of a fixed point of both a primitive substitution σ and a primitive substitution τ, then the dominant eigenvalues of the matrices of σ and of τ are multiplicatively dependent. This is the way we propose to generalize Cobham’s Theorem. ..."
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Cited by 13 (4 self)
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Abstract If a nonperiodic sequence X is the image by a morphism of a fixed point of both a primitive substitution σ and a primitive substitution τ, then the dominant eigenvalues of the matrices of σ and of τ are multiplicatively dependent. This is the way we propose to generalize Cobham’s Theorem. 1
An Extension of the CobhamSemënov Theorem
, 2000
"... Let , be two multiplicatively independent Pisot numbers, and let U , U , respectively. For every n 1, if A IN recognizable then A is de nable in hIN; +i. ..."
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Cited by 10 (1 self)
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Let , be two multiplicatively independent Pisot numbers, and let U , U , respectively. For every n 1, if A IN recognizable then A is de nable in hIN; +i.
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 2 (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.
A Survey of Arithmetical Definability
, 2002
"... We survey definability and decidability issues related to firstorder fragments of arithmetic, with a special emphasis on Presburger and Skolem arithmetic and their (un)decidable extensions. ..."
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Cited by 2 (0 self)
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We survey definability and decidability issues related to firstorder fragments of arithmetic, with a special emphasis on Presburger and Skolem arithmetic and their (un)decidable extensions.
Automata and Numeration Systems
"... This article is a short survey on the following problem: given a set X ` ..."
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