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- Cobham's theorem is a theorem in combinatorics on words that has important connections with number theory, notably transcendental numbers, and automata theory. Informally, the theorem gives the condition for the members of a set S of natural numbers written in bases b1 and base b2 to be recognised by finite automata. Specifically, consider bases b1 and b2 such that they are not powers of the same integer. Cobham's theorem states that S written in bases b1 and b2 is recognised by finite automata if and only if S is a finite union of arithmetic progressions. The theorem was proved by Alan Cobham in 1969 and has since given rise to many extensions and generalisations. (en)
- Le théorème de Cobham est un théorème de combinatoire des mots qui a des connexions importantes avec la théorie des nombres, et notamment des nombres transcendants, et avec la théorie des automates. Le théorème stipule que si les écritures, en deux bases multiplicativement indépendantes, d'un ensemble d'entiers naturels S sont des langages rationnels, alors l'ensemble S est une union finie de progressions arithmétiques. Le théorème a été prouvé par Alan Cobham en 1969. Depuis, il a donné lieu à de nombreuses extensions et généralisations. (fr)
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- 17771 (xsd:nonNegativeInteger)
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- Cobham's theorem is a theorem in combinatorics on words that has important connections with number theory, notably transcendental numbers, and automata theory. Informally, the theorem gives the condition for the members of a set S of natural numbers written in bases b1 and base b2 to be recognised by finite automata. Specifically, consider bases b1 and b2 such that they are not powers of the same integer. Cobham's theorem states that S written in bases b1 and b2 is recognised by finite automata if and only if S is a finite union of arithmetic progressions. The theorem was proved by Alan Cobham in 1969 and has since given rise to many extensions and generalisations. (en)
- Le théorème de Cobham est un théorème de combinatoire des mots qui a des connexions importantes avec la théorie des nombres, et notamment des nombres transcendants, et avec la théorie des automates. Le théorème stipule que si les écritures, en deux bases multiplicativement indépendantes, d'un ensemble d'entiers naturels S sont des langages rationnels, alors l'ensemble S est une union finie de progressions arithmétiques. Le théorème a été prouvé par Alan Cobham en 1969. Depuis, il a donné lieu à de nombreuses extensions et généralisations. (fr)
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- Cobham's theorem (en)
- Théorème de Cobham (fr)
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