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Narrow Proofs May Be Maximally Long
KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.ORCID iD: 0000-0002-2700-4285
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
URN: urn:nbn:se:kth:diva-191754DOI: 10.1145/2898435ISI: 000380019200005ScopusID: 2-s2.0-84973879640OAI: diva2:957548
Swedish Research Council, 621-2010-4797 621-2012-5645EU, FP7, Seventh Framework Programme, 279611

QC 20160902

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

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Nordström, Jakob
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