Relating equivalence and reducibility to sparse sets

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

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

2 Scopus citations

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 publicationProc 6 Annu Struct Complexity Theor
PublisherPubl by IEEE
Pages220-229
Number of pages10
ISBN (Print)0818622555, 9780818622557
StatePublished - Dec 1 1991
Externally publishedYes
EventProceedings of the 6th Annual Structure in Complexity Theory Conference - Chicago, IL, USA
Duration: Jun 30 1991Jul 3 1991

Publication series

NameProceedings of the Sixth Annual Structure in Complexity Theory Conference

Other

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

ASJC Scopus subject areas

  • Engineering(all)

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  • Cite this

    Allender, E., Hemachandra, L. A., Ogiwara, M., & Watanabe, O. (1991). Relating equivalence and reducibility to sparse sets. In Proc 6 Annu Struct Complexity Theor (pp. 220-229). (Proceedings of the Sixth Annual Structure in Complexity Theory Conference). Publ by IEEE.