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A Tight Karp-Lipton Collapse Result in Bounded Arithmetic

Beyersdorff, O and Mueller, S (2008) A Tight Karp-Lipton Collapse Result in Bounded Arithmetic. In: Kaminiski, M and Martini, S, (eds.) Proceedings of Computer Science Logic. 17th Annual Conference of the EACSL, 16-19 September 2008, Bertinoro, Italy. Lecture Notes in Computer Science, 5213 . Springer Verlag , 199 - 214 . ISBN 978-3-540-87530-7

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Abstract

Cook and Krajíček [9] have obtained the following Karp-Lipton result in bounded arithmetic: if the theory proves , then collapses to , and this collapse is provable in . Here we show the converse implication, thus answering an open question from [9]. We obtain this result by formalizing in a hard/easy argument of Buhrman, Chang, and Fortnow [3]. In addition, we continue the investigation of propositional proof systems using advice, initiated by Cook and Krajíček [9]. In particular, we obtain several optimal and even p-optimal proof systems using advice. We further show that these p-optimal systems are equivalent to natural extensions of Frege systems.

Item Type: Proceedings Paper
Copyright, Publisher and Additional Information: © 2008, Springer Verlag. This is an author produced version of a paper published in Proceedings of Computer Science Logic. Uploaded in accordance with the publisher's self-archiving policy.
Keywords: Karp-Lipton Theorem, Advice, Optimal Propositional Proof Systems, Bounded Arithmetic, Extended Frege
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds)
Depositing User: Symplectic Publications
Date Deposited: 10 Dec 2012 12:02
Last Modified: 09 Jun 2014 02:21
Published Version: http://dx.doi.org/10.1007/978-3-540-87531-4_16
Status: Published
Publisher: Springer Verlag
Identification Number: 10.1007/978-3-540-87531-4_16
URI: http://eprints.whiterose.ac.uk/id/eprint/74793

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