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.


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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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