TR05-011 Authors: Christian Glaßer, Mitsunori Ogihara, A. Pavan, Alan L. Selman, Liyu Zhang

Publication: 21st January 2005 21:47

Downloads: 2170

Keywords:

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 \cap coNP - P, then, for

every \epsilon > 0,

NP-complete sets are not 2^{n(1+\epsilon)}-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.