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 › peer-review

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 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

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title = "Autoreducibility, mitoticity, and immunity",

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.",

keywords = "Autoreducibility, Complete sets, Immunity, Mitoticity, Weak mitoticity",

author = "Christian Gla{\ss}er and Mitsunori Ogihara and A. Pavan and Selman, {Alan L.} and Liyu Zhang",

note = "Funding Information: Sci., vol. 3618, Springer, 2005, pp. 387–398]. * Corresponding author. E-mail addresses: glasser@informatik.uni-wuerzburg.de (C. Gla{\ss}er), ogihara@cs.rochester.edu (M. Ogihara), pavan@cs.iastate.edu (A. Pavan), selman@cse.buffalo.edu (A.L. Selman), lzhang7@cse.buffalo.edu (L. Zhang). 1 Research supported in part by NSF grants EIA-0080124, EIA-0205061, and NIH grant P30-AG18254. 2 Research supported in part by NSF grants CCR-0344817 and CCF-0430807. 3 Research supported in part by NSF grant CCR-0307077 and by the Alexander von Humboldt-Stiftung. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.",

year = "2007",

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doi = "10.1016/j.jcss.2006.10.020",

language = "English (US)",

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AU - Glaßer, Christian

AU - Ogihara, Mitsunori

AU - Pavan, A.

AU - Selman, Alan L.

AU - Zhang, Liyu

N1 - Funding Information: Sci., vol. 3618, Springer, 2005, pp. 387–398]. * Corresponding author. E-mail addresses: glasser@informatik.uni-wuerzburg.de (C. Glaßer), ogihara@cs.rochester.edu (M. Ogihara), pavan@cs.iastate.edu (A. Pavan), selman@cse.buffalo.edu (A.L. Selman), lzhang7@cse.buffalo.edu (L. Zhang). 1 Research supported in part by NSF grants EIA-0080124, EIA-0205061, and NIH grant P30-AG18254. 2 Research supported in part by NSF grants CCR-0344817 and CCF-0430807. 3 Research supported in part by NSF grant CCR-0307077 and by the Alexander von Humboldt-Stiftung. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.

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N2 - 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.

AB - 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.

KW - Autoreducibility

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KW - Mitoticity

KW - Weak mitoticity

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Autoreducibility, mitoticity, and immunity

Abstract

Keywords

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