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Narrow proofs may be spacious: Separating space and width in resolution
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.ORCID iD: 0000-0002-2700-4285
2006 (English)In: Proc. Annu. ACM Symp. Theory Comput., 2006, 507-516 p.Conference paper (Refereed)
Abstract [en]

The width of a resolution proof is the maximal number of literals in any clause of the proof. The space of a proof is the maximal number of clauses kept in memory simultaneously if the proof is only allowed to infer new clauses from clauses currently in memory. Both of these measures have previously been studied and related to the resolution refutation size of unsatisfiable CNF formulas. Also, the refutation space of a formula has been proven to be at least as large as the refutation width, but it has been open whether space can be separated from width or the two measures coincide asymptotically. We prove that there is a family of k-CNF formulas for which the refutation width in resolution is constant but the refutation space is non-constant, thus solving a problem mentioned in several previous papers.

Place, publisher, year, edition, pages
2006. 507-516 p.
, Proceedings of the Annual ACM Symposium on Theory of Computing, ISSN 0737-8017 ; 2006
Keyword [en]
Lower bound, Pebble game, Pebbling contradiction, Proof complexity, Resolution, Separation, Space, Width, Mathematical models, Set theory, Graph theory
National Category
Computer Science
URN: urn:nbn:se:kth:diva-155996ScopusID: 2-s2.0-33748114893ISBN: 1595931341ISBN: 9781595931344OAI: diva2:765805
38th Annual ACM Symposium on Theory of Computing, STOC'06, 21-23 May 2006, Seattle, WA, USA

QC 20141125

Available from: 2014-11-25 Created: 2014-11-17 Last updated: 2014-11-25Bibliographically approved

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