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

0369682 - MÚ 2012 RIV DE eng J - Journal Article
Thapen, Neil
Higher complexity search problems for bounded arithmetic and a formalized no-gap theorem.
Archive for Mathematical Logic. Roč. 50, 7-8 (2011), s. 665-680. ISSN 0933-5846. E-ISSN 1432-0665
R&D Projects: GA AV ČR IAA100190902; GA MŠMT LC505; GA MŠMT(CZ) 1M0545
Institutional research plan: CEZ:AV0Z10190503
Keywords : bounded arithmetic * proof complexity * search problems
Subject RIV: BA - General Mathematics
Impact factor: 0.341, year: 2011
http://www.springerlink.com/content/l19kr20362065t86/

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.
Permanent Link: http://hdl.handle.net/11104/0203691