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Narrow proofs may be spacious: separating space and width in resolution

Published: 21 May 2006 Publication History

Abstract

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.

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cover image ACM Conferences
STOC '06: Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing
May 2006
786 pages
ISBN:1595931341
DOI:10.1145/1132516
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 21 May 2006

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Author Tags

  1. lower bound
  2. pebble game
  3. pebbling contradiction
  4. proof complexity
  5. resolution
  6. separation
  7. space
  8. width

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STOC06
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STOC06: Symposium on Theory of Computing
May 21 - 23, 2006
WA, Seattle, USA

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  • (2014)The Complexity of Propositional ProofsBulletin of Symbolic Logic10.2178/bsl/120335087913:04(417-481)Online publication date: 15-Jan-2014
  • (2014)Total Space in ResolutionProceedings of the 2014 IEEE 55th Annual Symposium on Foundations of Computer Science10.1109/FOCS.2014.74(641-650)Online publication date: 18-Oct-2014
  • (2013)Pseudo-partitions, transversality and localityProceedings of the 4th conference on Innovations in Theoretical Computer Science10.1145/2422436.2422486(455-472)Online publication date: 9-Jan-2013
  • (2010)Different approaches to proof systemsProceedings of the 7th annual conference on Theory and Applications of Models of Computation10.1007/978-3-642-13562-0_6(50-59)Online publication date: 7-Jun-2010
  • (2008)Measuring the hardness of SAT instancesProceedings of the 23rd national conference on Artificial intelligence - Volume 110.5555/1619995.1620032(222-228)Online publication date: 13-Jul-2008
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  • (2008)Short Proofs May Be SpaciousProceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science10.1109/FOCS.2008.42(709-718)Online publication date: 25-Oct-2008
  • (2007)Game characterizations and the PSPACE-completeness of tree resolution spaceProceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic10.5555/2392389.2392438(527-541)Online publication date: 11-Sep-2007
  • (2007)Cryptography from SunspotsProceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science10.1109/FOCS.2007.22(249-259)Online publication date: 21-Oct-2007
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