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Unions of identifiable classes of total recursive functions

  • Kalvis Apsītis
  • Rūsinš Freivalds
  • Mārtinš Krikis
  • Raimonds Simanovskis
  • Juris Smotrovs
Submitted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 642)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Kalvis Apsītis
    • 1
  • Rūsinš Freivalds
    • 1
  • Mārtinš Krikis
    • 2
  • Raimonds Simanovskis
    • 1
  • Juris Smotrovs
    • 1
  1. 1.Institute of Mathematics and Computer ScienceUniversity of LatviaRigaLatvia
  2. 2.Computer Science DepartmentYale UniversityNew HavenUSA

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