Abstract
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{lunate} > 0, NP-complete sets are not 2n (1 + ε{lunate})-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.
Original language | English (US) |
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Pages (from-to) | 735-754 |
Number of pages | 20 |
Journal | Journal of Computer and System Sciences |
Volume | 73 |
Issue number | 5 |
DOIs | |
State | Published - Aug 2007 |
Externally published | Yes |
Keywords
- Autoreducibility
- Complete sets
- Immunity
- Mitoticity
- Weak mitoticity
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Networks and Communications
- Computational Theory and Mathematics
- Applied Mathematics