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

Lane A. Hemaspaandra; Leen Torenvliet

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arXiv · cs/0504096

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

Lane A. Hemaspaandra·Leen Torenvliet

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Abstract

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 Π_2^p/1-immune.

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Lane A. Hemaspaandra, Leen Torenvliet. 2005-12-07. P-Selectivity, Immunity, and the Power of One Bit. https://arxiv.org/abs/cs/0504096

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