Higher complexity search problems for bounded arithmetic and a formalized no-gap theorem

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F11%3A00369682" target="_blank" >RIV/67985840:_____/11:00369682 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00153-011-0240-0" target="_blank" >http://dx.doi.org/10.1007/s00153-011-0240-0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00153-011-0240-0" target="_blank" >10.1007/s00153-011-0240-0</a>

Result language
angličtina
Original language name
Higher complexity search problems for bounded arithmetic and a formalized no-gap theorem
Original language description
We give a new characterization of the strict "Sbjjb sentences provable using Sbkbk induction, for 1 j k. As a small application we show that, in a certain sense, Buss?s witnessing theorem for strict Sbkbk formulas already holds over the relatively weak theory PV. We exhibit a combinatorial principle with the property that a lower bound for it in constant-depth Frege would imply that the narrow CNFs with short depth j Frege refutations form a strict hierarchy with j, and hence that the relativized bounded arithmetic hierarchy can be separated by a family of "Sb1b1 sentences.
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
—

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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