5 research outputs found

    Autoreducibility of NP-Complete Sets

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    We study the polynomial-time autoreducibility of NP-complete sets and obtain separations under strong hypotheses for NP. Assuming there is a p-generic set in NP, we show the following: - For every k≥2k \geq 2, there is a kk-T-complete set for NP that is kk-T autoreducible, but is not kk-tt autoreducible or (k−1)(k-1)-T autoreducible. - For every k≥3k \geq 3, there is a kk-tt-complete set for NP that is kk-tt autoreducible, but is not (k−1)(k-1)-tt autoreducible or (k−2)(k-2)-T autoreducible. - There is a tt-complete set for NP that is tt-autoreducible, but is not btt-autoreducible. Under the stronger assumption that there is a p-generic set in NP ∩\cap coNP, we show: - For every k≥2k \geq 2, there is a kk-tt-complete set for NP that is kk-tt autoreducible, but is not (k−1)(k-1)-T autoreducible. Our proofs are based on constructions from separating NP-completeness notions. For example, the construction of a 2-T-complete set for NP that is not 2-tt-complete also separates 2-T-autoreducibility from 2-tt-autoreducibility

    Non-autoreducible Sets for NEXP

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    We investigate autoreducibility properties of complete sets for NEXP under different polynomial-time reductions. Specifically, we show that under some polynomial-time reductions there are complete sets for NEXP that are not autoreducible. We show that settling the question whether every complete set for NEXP under non-adaptative reduction is autoreducible under NOR-truth-table reduction either positively or negatively would lead to major results about the exponential time complexity classes

    Autoreducibility, Mitoticity, and Immunity

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    We show the following results regarding complete sets. • NP-complete sets and PSPACE-complete sets are many-one autoreducible. • Complete sets of any level of PH, MODPH, or the Boolean hierarchy over NP are many-one autoreducible. • EXP-complete sets are many-one mitotic. • NEXP-complete sets are weakly many-one mitotic. • PSPACE-complete sets are weakly Turing-mitotic. • If one-way permutations and quick pseudo-random generators exist, then NP-complete languages are m-mitotic. • If there is a tally language in NP ∩ coNP − P, then, for every ɛ> 0, NP-complete sets are not 2 n(1+ɛ)-immune. These results solve several of the open questions raised by Buhrman and Torenvliet in their 1994 survey paper on the structure of complete sets.
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