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Expander construction in VNC1

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10422307" target="_blank" >RIV/00216208:11320/20:10422307 - isvavai.cz</a>

  • Result on the web

    <a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ZXCpymFv9" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ZXCpymFv9</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/j.apal.2020.102796" target="_blank" >10.1016/j.apal.2020.102796</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Expander construction in VNC1

  • Original language description

    We give a combinatorial analysis (using edge expansion) of a variant of the iterative expander construction due to Reingold, Vadhan, and Wigderson [44], and show that this analysis can be formalized in the bounded arithmetic system VNC1 (corresponding to the &quot;NC1 reasoning&quot;). As a corollary, we prove the assumption made by Jerabek [28] that a construction of certain bipartite expander graphs can be formalized in VNC1. This in turn implies that every proof in Gentzen&apos;s sequent calculus LK of a monotone sequent can be simulated in the monotone version of LK (MLK) with only polynomial blowup in proof size, strengthening the quasipolynomial simulation result of Atserias, Galesi, and Pudlak [9]. (C) 2020 Elsevier B.V. All rights reserved.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Result continuities

  • Project

    <a href="/en/project/GX19-27871X" target="_blank" >GX19-27871X: Efficient approximation algorithms and circuit complexity</a><br>

  • Continuities

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

Others

  • Publication year

    2020

  • 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

    171

  • Issue of the periodical within the volume

    7

  • Country of publishing house

    NL - THE KINGDOM OF THE NETHERLANDS

  • Number of pages

    40

  • Pages from-to

    102796

  • UT code for WoS article

    000534581100002

  • EID of the result in the Scopus database

    2-s2.0-85081217459