Abstract
We show the following results regarding complete sets.
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NP-complete sets and PSPACE-complete sets are many-one autoreducible.
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Complete sets of any level of PH, MODPH, or the Boolean hierarchy over NP are many-one autoreducible.
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EXP-complete sets are many-one mitotic.
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NEXP-complete sets are weakly many-one mitotic.
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PSPACE-complete sets are weakly Turing-mitotic.
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If one-way permutations and quick pseudo-random generators exist, then NP-complete languages are m-mitotic.
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If there is a tally language in NP ∩ coNP - P, then, for every ε > 0, NP-complete sets are not 2n(1 + ε)-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.
A full version of this paper is available as ECCC Technical Report TR05-011.
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Glaßer, C., Ogihara, M., Pavan, A., Selman, A.L., Zhang, L. (2005). Autoreducibility, Mitoticity, and Immunity. In: Jȩdrzejowicz, J., Szepietowski, A. (eds) Mathematical Foundations of Computer Science 2005. MFCS 2005. Lecture Notes in Computer Science, vol 3618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549345_34
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DOI: https://doi.org/10.1007/11549345_34
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