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Narrow proofs may be maximally long
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.ORCID iD: 0000-0003-4003-3168
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.ORCID iD: 0000-0002-2700-4285
2014 (English)In: Proceedings of the Annual IEEE Conference on Computational Complexity, 2014, 286-297 p.Conference paper, Published paper (Refereed)
Abstract [en]

We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size nω(w). This shows that the simple counting argument that any formula refutable in width w must have a proof in size nO(ω) is essentially tight. Moreover, our lower bounds can be generalized to polynomial calculus resolution (PCR) and Sherali-Adams, implying that the corresponding size upper bounds in terms of degree and rank are tight as well. Our results do not extend all the way to Lasserre, however-the formulas we study have Lasserre proofs of constant rank and size polynomial in both n and w.

Place, publisher, year, edition, pages
2014. 286-297 p.
Keyword [en]
degree, Lasserre, length, PCR, polynomial calculus, proof complexity, rank, resolution, Sherali-Adams, size, width, Calculations, Computational complexity, Optical resolving power, Polynomials
National Category
Computer and Information Science
Identifiers
URN: urn:nbn:se:kth:diva-168868DOI: 10.1109/CCC.2014.36ISI: 000345759400028Scopus ID: 2-s2.0-84906667234ISBN: 9781479936267 (print)OAI: oai:DiVA.org:kth-168868DiVA: diva2:819714
Conference
29th Annual IEEE Conference on Computational Complexity, CCC 2014, 11 June 2014 through 13 June 2014, Vancouver, BC
Note

QC 20150611

Available from: 2015-06-11 Created: 2015-06-09 Last updated: 2015-06-11Bibliographically approved

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Lauria, MassimoNordström, Jakob

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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  • asciidoc
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