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Parameterized Bounded-Depth Frege Is not Optimal
2012 (English)In: ACM Transactions on Computation Theory, ISSN 1942-3454, E-ISSN 1942-3462, Vol. 4, no 3, 7- p.Article in journal (Refereed) Published
Abstract [en]

A general framework for parameterized proof complexity was introduced by Dantchev et al. [2007]. There, the authors show important results 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 this article 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 Ω(k) in parameterized bounded-depth Frege, and, as a special case, in dag-like Parameterized Resolution. This answers an open question posed in Dantchev et al. [2007]. 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 CNFs

Place, publisher, year, edition, pages
2012. Vol. 4, no 3, 7- p.
Keyword [en]
Bounded-depth Frege, Parameterized complexity, Proof complexity, Resolution
National Category
Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-112881DOI: 10.1145/2355580.2355582Scopus ID: 2-s2.0-84868675131OAI: oai:DiVA.org:kth-112881DiVA: diva2:587528
Note

QC 20130502

Available from: 2013-01-14 Created: 2013-01-14 Last updated: 2017-12-06Bibliographically approved

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Lauria, Massimo

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