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We show the following results regarding complete sets. • NP-complete sets and PSPACE-complete sets are polynomial-time many–one autoreducible.

• Complete sets of any level of PH, MODPH, or the Boolean hierarchy over NP are polynomial-time many–one autoreducible.

• EXP-complete sets are polynomial-time many–one mitotic.

• If there is a tally language in NP ∩ coNP − P , then, for every ϵ > 0 , NP-complete sets are not 2 n ( 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.


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Journal of Computer and System Sciences





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