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A Tight Karp-Lipton Collapse Result in Bounded Arithmetic

Beyersdorff, O and Mueller, S (2010) A Tight Karp-Lipton Collapse Result in Bounded Arithmetic. ACM Transactions on Computational Logic, 11 (4). ISSN 1529-3785

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Abstract

Cook and Krajícek have recently obtained the following Karp-Lipton collapse result in bounded arithmetic: if the theory PV proves NP⊆ P/poly, then the polynomial hierarchy collapses to the Boolean hierarchy, and this collapse is provable in PV. Here we show the converse implication, thus answering an open question posed by Cook and Krajíček. We obtain this result by formalizing in PV a hard/easy argument of Buhrman et al. [2003]. In addition, we continue the investigation of propositional proof systems using advice, initiated by Cook and Krajícek. In particular, we obtain several optimality results for proof systems using advice. We further show that these optimal systems are equivalent to natural extensions of Frege systems.

Item Type: Article
Keywords: Theory, Karp-Lipton theorem, advice, optimal propositional proof systems, bounded arithmetic, extended Frege
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 18 Jul 2012 13:09
Last Modified: 08 Feb 2013 17:39
Published Version: http://dx.doi.org/10.1145/1805950.1805952
Status: Published
Publisher: Association for Computing Machinery
Identification Number: 10.1145/1805950.1805952
URI: http://eprints.whiterose.ac.uk/id/eprint/74433

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