The provably total NP search problems of weak second order bounded arithmetic

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F11%3A00359552" target="_blank" >RIV/67985840:_____/11:00359552 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.apal.2010.12.002" target="_blank" >http://dx.doi.org/10.1016/j.apal.2010.12.002</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apal.2010.12.002" target="_blank" >10.1016/j.apal.2010.12.002</a>

Result language
angličtina
Original language name
The provably total NP search problems of weak second order bounded arithmetic
Original language description
We define a new NP search problem, the "local improvement" principle, about labellings of an acyclic, bounded-degree graph. We show that, provably in PV, it characterizes the for all Sigma(b)(1) consequences of V-2(1) and that natural restrictions of itcharacterize the for all Sigma(b)(1) consequences of U-2(1) and of the bounded arithmetic hierarchy. We also show that over V-0 it characterizes the for all Sigma(B)(0) consequences of V-1 and hence that, in some sense, a miniaturized version of the principle gives a new characterization of the for all Pi(b)(1) consequences of S-2(1). Throughout our search problems are "type-2" NP search problems, which take second-order objects as parameters: (c) 2011 Elsevier B.V. All rights reserved.
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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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