Circuit lower bounds in bounded arithmetics

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>

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
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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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)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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