Autoreducibility, mitoticity, and immunity

Christian Glaßer; Mitsunori Ogihara; A. Pavan; Alan L. Selman; Liyu Zhang

doi:10.1016/j.jcss.2006.10.020

Autoreducibility, mitoticity, and immunity

Christian Glaßer, Mitsunori Ogihara, A. Pavan, Alan L. Selman, Liyu Zhang

Research output: Contribution to journal › Article

14 Scopus citations

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 2^{n (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)
Pages (from-to)	735-754
Number of pages	20
Journal	Journal of Computer and System Sciences
Volume	73
Issue number	5
DOIs	https://doi.org/10.1016/j.jcss.2006.10.020
State	Published - Aug 1 2007
Externally published	Yes

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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

Cite this

Glaßer, C., Ogihara, M., Pavan, A., Selman, A. L., & Zhang, L. (2007). Autoreducibility, mitoticity, and immunity. Journal of Computer and System Sciences, 73(5), 735-754. https://doi.org/10.1016/j.jcss.2006.10.020

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10.1016/j.jcss.2006.10.020