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Narrow proofs may be maximally long
KTH, Skolan för datavetenskap och kommunikation (CSC), Teoretisk datalogi, TCS.ORCID-id: 0000-0003-4003-3168
KTH, Skolan för datavetenskap och kommunikation (CSC), Teoretisk datalogi, TCS.ORCID-id: 0000-0002-2700-4285
2014 (engelsk)Inngår i: Proceedings of the Annual IEEE Conference on Computational Complexity, 2014, s. 286-297Konferansepaper, Publicerat paper (Fagfellevurdert)
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.

sted, utgiver, år, opplag, sider
2014. s. 286-297
Emneord [en]
degree, Lasserre, length, PCR, polynomial calculus, proof complexity, rank, resolution, Sherali-Adams, size, width, Calculations, Computational complexity, Optical resolving power, Polynomials
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Identifikatorer
URN: urn:nbn:se:kth:diva-168868DOI: 10.1109/CCC.2014.36ISI: 000345759400028Scopus ID: 2-s2.0-84906667234ISBN: 9781479936267 (tryckt)OAI: oai:DiVA.org:kth-168868DiVA, id: diva2:819714
Konferanse
29th Annual IEEE Conference on Computational Complexity, CCC 2014, 11 June 2014 through 13 June 2014, Vancouver, BC
Merknad

QC 20150611

Tilgjengelig fra: 2015-06-11 Laget: 2015-06-09 Sist oppdatert: 2022-06-23bibliografisk kontrollert

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Lauria, MassimoNordström, Jakob

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