• DocumentCode
    2048267
  • Title

    NP-Hard Sets Are Exponentially Dense Unless coNP C NP/poly

  • Author

    Buhrman, Harry ; Hitchcock, John M.

  • Author_Institution
    CWI, Amsterdam
  • fYear
    2008
  • fDate
    23-26 June 2008
  • Firstpage
    1
  • Lastpage
    7
  • Abstract
    We show that hard sets S for NP must have exponential density, i.e. |S=n| ges 2nepsi for some isin > 0 and infinitely many n, unless coNP sube NP/poly and the polynomial-time hierarchy collapses. This result holds for Turing reductions that make n1-isin queries. In addition we study the instance complexity o/NP- hard problems and show that hard sets also have an exponential amount of instances that have instance complexity n for some sigma > 0. This result also holds for Turing reductions that make n1-isin queries.
  • Keywords
    computational complexity; NP-hard problem; NP-hard sets; Turing reductions; exponential density; instance complexity; polynomial-time hierarchy; Complexity theory; Computational complexity; Computer science; NP-complete problem; NP-hard problem; Polynomials; hard sets; instance complexity; polynomial advice;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Computational Complexity, 2008. CCC '08. 23rd Annual IEEE Conference on
  • Conference_Location
    College Park, MD
  • ISSN
    1093-0159
  • Print_ISBN
    978-0-7695-3169-4
  • Type

    conf

  • DOI
    10.1109/CCC.2008.21
  • Filename
    4558804
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=2048267