P-Selectivity, Immunity, and the Power of One Bit

  • Lane A. Hemaspaandra
  • Leen Torenvliet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3831)


We prove that P-sel, the class of all P-selective sets, is EXP-immune, but is not EXP/1-immune. That is, we prove that some infinite P-selective set has no infinite EXP-time subset, but we also prove that every infinite P-selective set has some infinite subset in EXP/1. Informally put, the immunity of P-sel is so fragile that it is pierced by a single bit of information.

The above claims follow from broader results that we obtain about the immunity of the P-selective sets. In particular, we prove that for every recursive function f, P-sel is DTIME(f)-immune. Yet we also prove that P-sel is not \({\it \Pi}^{p}_{2}\)/1-immune.


Turing Machine SIAM Journal Recursive Function Random Oracle Selector Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Lane A. Hemaspaandra
    • 1
  • Leen Torenvliet
    • 2
  1. 1.Department of Computer ScienceUniversity of RochesterRochesterUSA
  2. 2.ILLCUniversity of AmsterdamAmsterdamThe Netherlands

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