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Co-learnability and FIN-identifiability of enumerable classes of total recursive functions

  • Rūsiņš Freivalds
  • Dace Gobleja
  • Marek Karpinski
  • Carl H. Smith
Selected Papers Analogical and Inductive Inference
Part of the Lecture Notes in Computer Science book series (LNCS, volume 872)

Abstract

Co-learnability is an inference process where instead of producing the final result, the strategy produces all the natural numbers but one, and the omitted number is an encoding of the correct result. It has been proved in [1] that co-learnability of Goedel numbers is equivalent to EX-identifiability. We consider co-learnability of indices in recursively enumerable (r.e.) numberings. The power of co-learnability depends on the numberings used. Every r.e. class of total recursive functions is co-learnable in some r.e. numbering. FIN-identifiable classes are co-learnable in all r.e. numberings, and classes containing a function being accumulation point are not co-learnable in some r.e. numberings. Hence it was conjectured in [1] that only FIN-identifiable classes are co-learnable in all r.e. numberings. The conjecture is disproved in this paper using a sophisticated construction by V.L. Selivanov.

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Rūsiņš Freivalds
    • 1
  • Dace Gobleja
    • 2
  • Marek Karpinski
    • 3
    • 4
  • Carl H. Smith
    • 5
  1. 1.Institute of Mathematics and Computer ScienceUniversity of LatviaRigaLatvia
  2. 2.Institute of Mathematics and Computer ScienceUniversity of LatviaRigaLatvia
  3. 3.Department of Computer ScienceUniversity of BonnBonn
  4. 4.The International Computer Science InstituteBerkeley
  5. 5.Department of Computer ScienceUniversity of MarylandCollege ParkUSA

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