Abstract
J.Barzdin [Bar74] has proved that there are classes of total recursive functions which are EX-identifiable but their union is not. We prove that there are no 3 classes U1, U2, U3 such that U1∪U2,U1∪U3 and U2∪U3 would be in EX but U1∪U2∪U3∉ EX. For FIN-identification there are 3 classes with the above-mentioned property and there are no 4 classes U1, U2, U3, U4 such that all 4 unions of triples of these classes would be identifiable but the union of all 4 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 properly.
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© 1992 Springer-Verlag Berlin Heidelberg
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Apsītis, K., Freivalds, R., Krikis, M., Simanovskis, R., Smotrovs, J. (1992). Unions of identifiable classes of total recursive functions. In: Jantke, K.P. (eds) Analogical and Inductive Inference. AII 1992. Lecture Notes in Computer Science, vol 642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56004-1_7
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DOI: https://doi.org/10.1007/3-540-56004-1_7
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