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 |
| Academic Units: | The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science |
| Depositing User: | Symplectic Publications |
| Date Deposited: | 10 Dec 2012 12:02 |
| Last Modified: | 08 Feb 2013 17:41 |
| 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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