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Higher complexity search problems for bounded arithmetic and a formalized no-gap theorem
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SYSNO ASEP 0369682 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Higher complexity search problems for bounded arithmetic and a formalized no-gap theorem Author(s) Thapen, Neil (MU-W) RID, SAI Source Title Archive for Mathematical Logic. - : Springer - ISSN 0933-5846
Roč. 50, 7-8 (2011), s. 665-680Number of pages 16 s. Language eng - English Country DE - Germany Keywords bounded arithmetic ; proof complexity ; search problems Subject RIV BA - General Mathematics R&D Projects IAA100190902 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) LC505 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) 1M0545 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000300094700001 EID SCOPUS 80054119010 DOI 10.1007/s00153-011-0240-0 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2012
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