Change search
ReferencesLink to record
Permanent link

Direct link
Narrow Proofs May Be Maximally Long
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.ORCID iD: 0000-0002-2700-4285
2016 (English)In: ACM Transactions on Computational Logic, ISSN 1529-3785, E-ISSN 1557-945X, Vol. 17, no 3, 19Article in journal (Refereed) Published
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 n(Omega(w)). This shows that the simple counting argument that any formula refutable in width w must have a proof in size n(O(w)) is essentially tight. Moreover, our lower bound generalizes to polynomial calculus resolution and Sherali-Adams, implying that the corresponding size upper bounds in terms of degree and rank are tight as well. The lower bound does not extend all the way to Lasserre, however, since we show that there the formulas we study have proofs of constant rank and size polynomial in both n and w.

Place, publisher, year, edition, pages
Association for Computing Machinery (ACM), 2016. Vol. 17, no 3, 19
Keyword [en]
Proof complexity, resolution, width, polynomial calculus, polynomial calculus resolution, PCR, Sherali-Adams, SAR, degree
National Category
Other Computer and Information Science
Identifiers
URN: urn:nbn:se:kth:diva-191754DOI: 10.1145/2898435ISI: 000380019200005ScopusID: 2-s2.0-84973879640OAI: oai:DiVA.org:kth-191754DiVA: diva2:957548
Funder
Swedish Research Council, 621-2010-4797 621-2012-5645EU, FP7, Seventh Framework Programme, 279611
Note

QC 20160902

Available from: 2016-09-02 Created: 2016-09-02 Last updated: 2016-09-02Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Nordström, Jakob
By organisation
Theoretical Computer Science, TCS
In the same journal
ACM Transactions on Computational Logic
Other Computer and Information Science

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 3 hits
ReferencesLink to record
Permanent link

Direct link