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 "NC1 reasoning"). 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'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
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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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
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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