Beyersdorff, O, Galesi, N, Lauria, M et al. (1 more author) (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, 04-08 Jul 2011, Zurich, Switzerland. Lecture Notes in Computer Science, 6755 (Part 1). Springer Verlag , 630 - 641 . ISBN 978-3-642-22005-0
Abstract
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.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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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 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (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: | 19 Dec 2022 13:24 |
Published Version: | http://dx.doi.org/10.1007/978-3-642-22006-7_53 |
Status: | Published |
Publisher: | Springer Verlag |
Series Name: | Lecture Notes in Computer Science |
Identification Number: | 10.1007/978-3-642-22006-7_53 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:74804 |