Počet záznamů: 1

A New Characterization of ACC(0) and Probabilistic CC0

  1. 1.
    0352500 - MU-W 2011 RIV CH eng J - Článek v odborném periodiku
    Hansen, A. K. - Koucký, Michal
    A New Characterization of ACC(0) and Probabilistic CC0.
    Computational Complexity. Roč. 19, č. 2 (2010), s. 211-234 ISSN 1016-3328.
    [24th Annual IEEE Conference on Computational Complexity. Paris, 15.07.2009-18.07.2009]
    Grant CEP: GA ČR GAP202/10/0854; GA MŠk(CZ) 1M0545; GA AV ČR IAA100190902
    Výzkumný záměr: CEZ:AV0Z10190503
    Klíčová slova: bounded depth circuits * counting circuits * arithmetic circuits * complexity classes
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 1.450, rok: 2010
    http://link.springer.com/article/10.1007%2Fs00037-010-0287-z

    Barrington, Straubing and Thérien (1990) conjectured that the Boolean AND function can not be computed by polynomial size constant depth circuits built from modular counting gates, i.e., by CC^0 circuits. In this work we show that the AND function can be computed by uniform probabilistic CC^0 circuits that use only O(log n) random bits. This may be viewed as evidence contrary to the conjecture. As a consequence of our construction we get that all of ACC^0 can be computed by probabilistic CC^0 circuits that use only O(/log n) random bits. Thus, if one were able to derandomize such circuits, one would obtain a collapse of circuit classes giving ACC^0=CC^0. We present a derandomization of probabilistic CC^0 circuits using AND and OR gates to obtain ACC^0 = AND /circ OR /circ CC^0 = OR /circ AND /circ CC^0. (AND and OR gates of sublinear fan-in suffice in non-uniform setting.)
    Trvalý link: http://hdl.handle.net/11104/0191994
    Název souboruStaženoVelikostKomentářVerzePřístup
    Koucky3.pdf1539.5 KBVydavatelský postprintvyžádat