Relating equivalence and reducibility to sparse sets

Eric Allender, Lane A. Hemachandra, Mitsunori Ogihara, Osamu Watanabe

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

2 Citations (Scopus)

Abstract

For various polynomial-time reducibilities r, the authors ask whether being r-reducible to a sparse set is a broader notion than being r-equivalent to a sparse set. Although distinguishing equivalence and reducibility to sparse sets, for many-one or 1-truth-table reductions, would imply that P ≠ NP, the authors show that for k-truth-table reductions, k ≥ 2, equivalence and reducibility to sparse sets provably differ. Though R. Gavaldaand D. Watanabe have shown that, for any polynomial-time computable unbounded function f(·), some sets f(n)-truth-table reducible to sparse sets are not even Turing equivalent to sparse sets, the authors show that extending their result to the 2-truth-table case would provide a proof that P ≠ NP. Additionally, the authors study the relative power of different notions of reducibility and show that disjunctive and conjunctive truth-table reductions to sparse sets are surprisingly powerful, refuting a conjecture of K. Ko (1989).

Original languageEnglish (US)
Title of host publicationProceedings of the Sixth Annual Structure in Complexity Theory Conference
PublisherPubl by IEEE
Pages220-229
Number of pages10
ISBN (Print)0818622555, 9780818622557
StatePublished - 1991
Externally publishedYes
EventProceedings of the 6th Annual Structure in Complexity Theory Conference - Chicago, IL, USA
Duration: Jun 30 1991Jul 3 1991

Other

OtherProceedings of the 6th Annual Structure in Complexity Theory Conference
CityChicago, IL, USA
Period6/30/917/3/91

Fingerprint

Polynomials

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Allender, E., Hemachandra, L. A., Ogihara, M., & Watanabe, O. (1991). Relating equivalence and reducibility to sparse sets. In Proceedings of the Sixth Annual Structure in Complexity Theory Conference (pp. 220-229). Publ by IEEE.

Relating equivalence and reducibility to sparse sets. / Allender, Eric; Hemachandra, Lane A.; Ogihara, Mitsunori; Watanabe, Osamu.

Proceedings of the Sixth Annual Structure in Complexity Theory Conference. Publ by IEEE, 1991. p. 220-229.

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

Allender, E, Hemachandra, LA, Ogihara, M & Watanabe, O 1991, Relating equivalence and reducibility to sparse sets. in Proceedings of the Sixth Annual Structure in Complexity Theory Conference. Publ by IEEE, pp. 220-229, Proceedings of the 6th Annual Structure in Complexity Theory Conference, Chicago, IL, USA, 6/30/91.
Allender E, Hemachandra LA, Ogihara M, Watanabe O. Relating equivalence and reducibility to sparse sets. In Proceedings of the Sixth Annual Structure in Complexity Theory Conference. Publ by IEEE. 1991. p. 220-229
Allender, Eric ; Hemachandra, Lane A. ; Ogihara, Mitsunori ; Watanabe, Osamu. / Relating equivalence and reducibility to sparse sets. Proceedings of the Sixth Annual Structure in Complexity Theory Conference. Publ by IEEE, 1991. pp. 220-229
@inproceedings{7a79a0223d024e7b928adff8da3fe215,
title = "Relating equivalence and reducibility to sparse sets",
abstract = "For various polynomial-time reducibilities r, the authors ask whether being r-reducible to a sparse set is a broader notion than being r-equivalent to a sparse set. Although distinguishing equivalence and reducibility to sparse sets, for many-one or 1-truth-table reductions, would imply that P ≠ NP, the authors show that for k-truth-table reductions, k ≥ 2, equivalence and reducibility to sparse sets provably differ. Though R. Gavaldaand D. Watanabe have shown that, for any polynomial-time computable unbounded function f(·), some sets f(n)-truth-table reducible to sparse sets are not even Turing equivalent to sparse sets, the authors show that extending their result to the 2-truth-table case would provide a proof that P ≠ NP. Additionally, the authors study the relative power of different notions of reducibility and show that disjunctive and conjunctive truth-table reductions to sparse sets are surprisingly powerful, refuting a conjecture of K. Ko (1989).",
author = "Eric Allender and Hemachandra, {Lane A.} and Mitsunori Ogihara and Osamu Watanabe",
year = "1991",
language = "English (US)",
isbn = "0818622555",
pages = "220--229",
booktitle = "Proceedings of the Sixth Annual Structure in Complexity Theory Conference",
publisher = "Publ by IEEE",

}

TY - GEN

T1 - Relating equivalence and reducibility to sparse sets

AU - Allender, Eric

AU - Hemachandra, Lane A.

AU - Ogihara, Mitsunori

AU - Watanabe, Osamu

PY - 1991

Y1 - 1991

N2 - For various polynomial-time reducibilities r, the authors ask whether being r-reducible to a sparse set is a broader notion than being r-equivalent to a sparse set. Although distinguishing equivalence and reducibility to sparse sets, for many-one or 1-truth-table reductions, would imply that P ≠ NP, the authors show that for k-truth-table reductions, k ≥ 2, equivalence and reducibility to sparse sets provably differ. Though R. Gavaldaand D. Watanabe have shown that, for any polynomial-time computable unbounded function f(·), some sets f(n)-truth-table reducible to sparse sets are not even Turing equivalent to sparse sets, the authors show that extending their result to the 2-truth-table case would provide a proof that P ≠ NP. Additionally, the authors study the relative power of different notions of reducibility and show that disjunctive and conjunctive truth-table reductions to sparse sets are surprisingly powerful, refuting a conjecture of K. Ko (1989).

AB - For various polynomial-time reducibilities r, the authors ask whether being r-reducible to a sparse set is a broader notion than being r-equivalent to a sparse set. Although distinguishing equivalence and reducibility to sparse sets, for many-one or 1-truth-table reductions, would imply that P ≠ NP, the authors show that for k-truth-table reductions, k ≥ 2, equivalence and reducibility to sparse sets provably differ. Though R. Gavaldaand D. Watanabe have shown that, for any polynomial-time computable unbounded function f(·), some sets f(n)-truth-table reducible to sparse sets are not even Turing equivalent to sparse sets, the authors show that extending their result to the 2-truth-table case would provide a proof that P ≠ NP. Additionally, the authors study the relative power of different notions of reducibility and show that disjunctive and conjunctive truth-table reductions to sparse sets are surprisingly powerful, refuting a conjecture of K. Ko (1989).

UR - http://www.scopus.com/inward/record.url?scp=0026398366&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026398366&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0818622555

SN - 9780818622557

SP - 220

EP - 229

BT - Proceedings of the Sixth Annual Structure in Complexity Theory Conference

PB - Publ by IEEE

ER -