The power of procrastination in inductive inference: How it depends on used ordinal notations

  • Andris Ambainis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 904)


We consider inductive inference with procrastination. Usually it is defined using constructive ordinals. For constructive ordinals there exist many different systems of notations. In this paper we study how the power of inductive inference depends on used system of notations.

We prove that for constructive ordinals α smaller than ω2 each set of total recursive functions which is EX α -identifiable in one system of notations is EX α -identifiable in arbitrary system of notations. For \(EX_{\omega ^2 } \)-identification such property does not hold.

Also, we consider the question whether, among all systems of notations there exists the strongest and the weakest system. We prove that there exist such system of notations S that arbitrary set of functions which is EX α -identifiable in some system of notations is EX α -identifiable in S, too. If ω2≤α<2ω2, there exist such system A that each set of functions which is EX α -identifiable in A is EX α -identifiable in arbitrary system of notations.

Further, we consider possible tradeoffs between using larger ordinals and using more complicated systems of notations. We prove that, in general, there are no such tradeoffs.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Andris Ambainis
    • 1
  1. 1.Institute of Mathematics and Computer ScienceUniversity of LatviaRigaLatvia

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