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Circuit lower bounds in bounded arithmetics

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F15%3A00438367" target="_blank" >RIV/67985840:_____/15:00438367 - isvavai.cz</a>

  • Alternative codes found

    RIV/00216208:11320/15:10317954

  • Result on the web

    <a href="http://dx.doi.org/10.1016/j.apal.2014.08.004" target="_blank" >http://dx.doi.org/10.1016/j.apal.2014.08.004</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/j.apal.2014.08.004" target="_blank" >10.1016/j.apal.2014.08.004</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Circuit lower bounds in bounded arithmetics

  • Original language description

    We prove that T-Nc(1), the true universal first-order theory in the language containing names for all uniform NC1 algorithms, cannot prove that for sufficiently large n, SAT is not computable by circuits of size n(4kc) where k >= 1, c >= 2 unless each function f is an element of SIZE(n(k)) can be approximated by formulas {Fn}(n=1)(infinity) of subexponential size 2(O(n1/c)) with subexponential advantage: P-x is an element of(0,1)(n) (F-n(x) = f(x)) >= 1/2+1/2(O)(n(1/c)). Unconditionally, V cannot provethat for sufficiently large n, SAT does not have circuits of size n(logn). The proof is based on an interpretation of Krajicek's proof (Krajicek, 2011 [15]) that certain NW-generators are hard for T-PV, the true universal theory in the language containing names for all p-time algorithms.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/IAA100190902" target="_blank" >IAA100190902: Mathematical logic, complexity, and algorithms</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2015

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Annals of Pure and Applied Logic

  • ISSN

    0168-0072

  • e-ISSN

  • Volume of the periodical

    166

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    NL - THE KINGDOM OF THE NETHERLANDS

  • Number of pages

    17

  • Pages from-to

    29-45

  • UT code for WoS article

    000345480600002

  • EID of the result in the Scopus database