Separating the notions of self- and autoreducibility

Piotr Faliszewski, Mitsunori Ogihara

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

1 Citation (Scopus)

Abstract

Recently Glaßer et al. have shown that for many classes C including PSPACE and NP it holds that all of its nontrivial many-one complete languages are autoreducible. This immediately raises the question of whether all many-one complete languages are Turing self-reducible for such classes C. This paper considers a simpler version of this question-whether all PSPACE-complete (NP-complete) languages are length-decreasing self-reducible. We show that if all PSPACE-complete languages are length-decreasing self-reducible then PSPACE = P and that if all NP-complete languages are length-decreasing self-reducible then NP = P. The same type of result holds for many other natural complexity classes. In particular, we show that (1) not all NL-complete sets are logspace length-decreasing self-reducible, (2) unconditionally not all PSPACE-complete languages are logpsace length-decreasing self-reducible, and (3) unconditionally not all EXP-complete languages are polynomial-time length-decreasing self-reducible.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science
EditorsJ. Jedrzejowicz, A. Szepietowski
Pages308-315
Number of pages8
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

Fingerprint

Polynomials

ASJC Scopus subject areas

  • Computer Science (miscellaneous)

Cite this

Faliszewski, P., & Ogihara, M. (2005). Separating the notions of self- and autoreducibility. In J. Jedrzejowicz, & A. Szepietowski (Eds.), Lecture Notes in Computer Science (Vol. 3618, pp. 308-315)

Separating the notions of self- and autoreducibility. / Faliszewski, Piotr; Ogihara, Mitsunori.

Lecture Notes in Computer Science. ed. / J. Jedrzejowicz; A. Szepietowski. Vol. 3618 2005. p. 308-315.

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

Faliszewski, P & Ogihara, M 2005, Separating the notions of self- and autoreducibility. in J Jedrzejowicz & A Szepietowski (eds), Lecture Notes in Computer Science. vol. 3618, pp. 308-315, 30th International Symposium on Mathematical Foundations of Computer Science 2005, MFCS 2005, Gdansk, Poland, 8/29/05.
Faliszewski P, Ogihara M. Separating the notions of self- and autoreducibility. In Jedrzejowicz J, Szepietowski A, editors, Lecture Notes in Computer Science. Vol. 3618. 2005. p. 308-315
Faliszewski, Piotr ; Ogihara, Mitsunori. / Separating the notions of self- and autoreducibility. Lecture Notes in Computer Science. editor / J. Jedrzejowicz ; A. Szepietowski. Vol. 3618 2005. pp. 308-315
@inproceedings{0ebe75c1515442bd8c26a0af201fd532,
title = "Separating the notions of self- and autoreducibility",
abstract = "Recently Gla{\ss}er et al. have shown that for many classes C including PSPACE and NP it holds that all of its nontrivial many-one complete languages are autoreducible. This immediately raises the question of whether all many-one complete languages are Turing self-reducible for such classes C. This paper considers a simpler version of this question-whether all PSPACE-complete (NP-complete) languages are length-decreasing self-reducible. We show that if all PSPACE-complete languages are length-decreasing self-reducible then PSPACE = P and that if all NP-complete languages are length-decreasing self-reducible then NP = P. The same type of result holds for many other natural complexity classes. In particular, we show that (1) not all NL-complete sets are logspace length-decreasing self-reducible, (2) unconditionally not all PSPACE-complete languages are logpsace length-decreasing self-reducible, and (3) unconditionally not all EXP-complete languages are polynomial-time length-decreasing self-reducible.",
author = "Piotr Faliszewski and Mitsunori Ogihara",
year = "2005",
language = "English (US)",
volume = "3618",
pages = "308--315",
editor = "J. Jedrzejowicz and A. Szepietowski",
booktitle = "Lecture Notes in Computer Science",

}

TY - GEN

T1 - Separating the notions of self- and autoreducibility

AU - Faliszewski, Piotr

AU - Ogihara, Mitsunori

PY - 2005

Y1 - 2005

N2 - Recently Glaßer et al. have shown that for many classes C including PSPACE and NP it holds that all of its nontrivial many-one complete languages are autoreducible. This immediately raises the question of whether all many-one complete languages are Turing self-reducible for such classes C. This paper considers a simpler version of this question-whether all PSPACE-complete (NP-complete) languages are length-decreasing self-reducible. We show that if all PSPACE-complete languages are length-decreasing self-reducible then PSPACE = P and that if all NP-complete languages are length-decreasing self-reducible then NP = P. The same type of result holds for many other natural complexity classes. In particular, we show that (1) not all NL-complete sets are logspace length-decreasing self-reducible, (2) unconditionally not all PSPACE-complete languages are logpsace length-decreasing self-reducible, and (3) unconditionally not all EXP-complete languages are polynomial-time length-decreasing self-reducible.

AB - Recently Glaßer et al. have shown that for many classes C including PSPACE and NP it holds that all of its nontrivial many-one complete languages are autoreducible. This immediately raises the question of whether all many-one complete languages are Turing self-reducible for such classes C. This paper considers a simpler version of this question-whether all PSPACE-complete (NP-complete) languages are length-decreasing self-reducible. We show that if all PSPACE-complete languages are length-decreasing self-reducible then PSPACE = P and that if all NP-complete languages are length-decreasing self-reducible then NP = P. The same type of result holds for many other natural complexity classes. In particular, we show that (1) not all NL-complete sets are logspace length-decreasing self-reducible, (2) unconditionally not all PSPACE-complete languages are logpsace length-decreasing self-reducible, and (3) unconditionally not all EXP-complete languages are polynomial-time length-decreasing self-reducible.

UR - http://www.scopus.com/inward/record.url?scp=26844460241&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26844460241&partnerID=8YFLogxK

M3 - Conference contribution

VL - 3618

SP - 308

EP - 315

BT - Lecture Notes in Computer Science

A2 - Jedrzejowicz, J.

A2 - Szepietowski, A.

ER -