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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Cook and Krajíček  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 . We obtain this result by formalizing in a hard/easy argument of Buhrman, Chang, and Fortnow . In addition, we continue the investigation of propositional proof systems using advice, initiated by Cook and Krajíček . 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|