Modèles de calcul sur les réels, résultats de comparaison. (Computation on the reals.Comparison of some models)

Il existe de nombreux modeles de calcul sur les reels. Ces differents modeles calculent diverses fonctions, certains sont plus puissants que d'autres, certains sont deux a deux incomparables. Le calcul sur les reels est donc de ce point de vue bien different du calcul sur les entiers qui est unifie par la these de Church-Turing affirmant que tous les modeles raisonnables calculent les memes fonctions. Nous montrons des equivalences entre les fonctions recursivement calculables et une certaine classe de fonctions R-recursives et entre les fonctions GPAC-calculables et les fonctions recursivement calculables. Nous montrons egalement une hierarchie de classes de fonctions R-recursives qui caracterisent les fonctions elementairement calculables, les fonctions de la hierarchie de Grzegorczyk et les fonctions recursivement calculables a l'aide d'un operateur de limite. Ces resultats constituent donc une avancee vers une eventuelle unification des modeles de calcul sur les reels

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