Autoreducibility, mitoticity, and immunity

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Citations (Scopus)

Abstract

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 ε > 0, NP-complete sets are not 2 n(1+ε)- 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 languageEnglish (US)
Title of host publicationLecture Notes in Computer Science
EditorsJ. Jedrzejowicz, A. Szepietowski
Pages387-398
Number of pages12
Volume3618
StatePublished - 2005
Externally publishedYes
Event30th International Symposium on Mathematical Foundations of Computer Science 2005, MFCS 2005 - Gdansk, Poland
Duration: Aug 29 2005Sep 2 2005

Other

Other30th International Symposium on Mathematical Foundations of Computer Science 2005, MFCS 2005
CountryPoland
CityGdansk
Period8/29/059/2/05

ASJC Scopus subject areas

  • Computer Science (miscellaneous)

Cite this

Glaßer, C., Ogihara, M., Pavan, A., Selman, A. L., & Zhang, L. (2005). Autoreducibility, mitoticity, and immunity. In J. Jedrzejowicz, & A. Szepietowski (Eds.), Lecture Notes in Computer Science (Vol. 3618, pp. 387-398)

Autoreducibility, mitoticity, and immunity. / Glaßer, Christian; Ogihara, Mitsunori; Pavan, A.; Selman, Alan L.; Zhang, Liyu.

Lecture Notes in Computer Science. ed. / J. Jedrzejowicz; A. Szepietowski. Vol. 3618 2005. p. 387-398.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Glaßer, C, Ogihara, M, Pavan, A, Selman, AL & Zhang, L 2005, Autoreducibility, mitoticity, and immunity. in J Jedrzejowicz & A Szepietowski (eds), Lecture Notes in Computer Science. vol. 3618, pp. 387-398, 30th International Symposium on Mathematical Foundations of Computer Science 2005, MFCS 2005, Gdansk, Poland, 8/29/05.
Glaßer C, Ogihara M, Pavan A, Selman AL, Zhang L. Autoreducibility, mitoticity, and immunity. In Jedrzejowicz J, Szepietowski A, editors, Lecture Notes in Computer Science. Vol. 3618. 2005. p. 387-398
Glaßer, Christian ; Ogihara, Mitsunori ; Pavan, A. ; Selman, Alan L. ; Zhang, Liyu. / Autoreducibility, mitoticity, and immunity. Lecture Notes in Computer Science. editor / J. Jedrzejowicz ; A. Szepietowski. Vol. 3618 2005. pp. 387-398
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