Unions Of Identifiable Classes Of Total Recursive Functions
AII '92: Proceedings of the International Workshop on Analogical and Inductive Inference(1992)
摘要
J.Barzdin [Bar74] has proved that there are classes of total recursive functions which ore EX-identifiable but their union is not. We prove that there are no 3 classes U1, U2, U3 such that U1 or U2, U1 or U3, or U2 or U3 would be in EX but U1 or U2 or U3 is-not-an-element-of EX. For FIN-identification there are 3 classes with the above-mentioned property and there are no A classes U1, U2, U3, U4 such that all 4 unions of triples of these classes would be identifiable but the union of all A classes would not. For identification with no more than p minchanges a (2p+2-1)-tuple of such classes do exist but there is no (2P+2)-tuple with the above-mentioned property.
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关键词
Identifiable Classes,Total Recursive Functions
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