Autoreducibility, Mitoticity, and Immunity

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 > 0, NP-complete sets are not 2n(1+ ) -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.

• Type: Conference
• Year: 2005
• Where: MFCS
• Authors: Christian Glaßer, Mitsunori Ogihara, Aduri Pavan, Alan L. Selman, Liyu Zhang
• Keywords: Complete Sets, MFCS 2005, NP-complete Sets, PSPACE-complete Sets