P-Selectivity, Immunity, and the Power of One Bit
نویسندگان
چکیده
We prove that P-sel, the class of all P-selective sets, is EXPimmune, 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 /1-immune.
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