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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 87 (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 15 (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
CobhamSemenov theorem and Ndsubshifts
 Theoret. Comput. Sci
"... We give a new proof of the Cobham’s first theorem using ideas from symbolic dynamics and of the CobhamSemenov theorem (in the primitive case) using ideas from tiling dynamics. 1 ..."
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Cited by 4 (1 self)
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We give a new proof of the Cobham’s first theorem using ideas from symbolic dynamics and of the CobhamSemenov theorem (in the primitive case) using ideas from tiling dynamics. 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 3 (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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