• DocumentCode
    2932908
  • Title

    A lower bound for perceptrons and an oracle separation of the PP PH hierarchy

  • Author

    Berg, Christer ; Ulfberg, Staffan

  • Author_Institution
    Dept. of Numerical Anal. & Comput. Sci., R. Inst. of Technol., Stockholm, Sweden
  • fYear
    1997
  • fDate
    24-27 Jun 1997
  • Firstpage
    165
  • Lastpage
    172
  • Abstract
    We show that there are functions computable by linear size boolean circuits of depth k that require superpolynomial size perceptrons of depth k-1, for k<log n/(6 log log n). This result implies the existence of an oracle A such that Σkp,A⊄PPΣ(k-2 p,A) and in particular this oracle separates the levels in the PPPH hierarchy. Using the same ideas, we show a lower bound for another function, which makes it possible to strengthen the oracle separation to Δkp,A⊄PPΣ(k-2 p,A)
  • Keywords
    Boolean functions; computational complexity; logic circuits; perceptrons; PPPH hierarchy; linear size boolean circuits; lower bound; oracle separation; perceptrons; superpolynomial size perceptrons; Circuits; Ear; Numerical analysis; Polynomials;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Computational Complexity, 1997. Proceedings., Twelfth Annual IEEE Conference on (Formerly: Structure in Complexity Theory Conference)
  • Conference_Location
    Ulm
  • ISSN
    1093-0159
  • Print_ISBN
    0-8186-7907-7
  • Type

    conf

  • DOI
    10.1109/CCC.1997.612312
  • Filename
    612312
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=2932908