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Parameterized bounded-depth Frege is not optimal

Beyersdorff, O, Galesi, N, Lauria, M and Razborov, A (2011) Parameterized bounded-depth Frege is not optimal. In: Aceto, L, Henzinger, M and Sgall, J, (eds.) Automata, languages and programmes, proceedings ICALP. ICALP 2011, 4-8 July 2011, Zurich, Switzerland. Lecture Notes in Computer Science, 6755 (Part 1). Springer Verlag , 630 - 641 . ISBN 978-3-642-22005-0

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A general framework for parameterized proof complexity was introduced by Dantchev, Martin, and Szeider [9]. There the authors concentrate on tree-like Parameterized Resolution-a parameterized version of classical Resolution-and their gap complexity theorem implies lower bounds for that system. The main result of the present paper significantly improves upon this by showing optimal lower bounds for a parameterized version of bounded-depth Frege. More precisely, we prove that the pigeonhole principle requires proofs of size n in parameterized bounded-depth Frege, and, as a special case, in dag-like Parameterized Resolution. This answers an open question posed in [9]. In the opposite direction, we interpret a well-known technique for FPT algorithms as a DPLL procedure for Parameterized Resolution. Its generalization leads to a proof search algorithm for Parameterized Resolution that in particular shows that tree-like Parameterized Resolution allows short refutations of all parameterized contradictions given as bounded-width CNF's.

Item Type: Proceedings Paper
Copyright, Publisher and Additional Information: © 2011, Springer Verlag. This is an author produced version of a paper published in Automata, languages and programmes. Uploaded in accordance with the publisher's self-archiving policy. The original publication is available at www.springerlink.com
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 14:50
Last Modified: 10 Jun 2014 06:47
Published Version: http://dx.doi.org/10.1007/978-3-642-22006-7_53
Status: Published
Publisher: Springer Verlag
Identification Number: 10.1007/978-3-642-22006-7_53
URI: http://eprints.whiterose.ac.uk/id/eprint/74804

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