PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Rights accessOpen Access
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¿(w). This shows that the simple counting argument that any formula refutable in width w must have a proof in size nO(¿) 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.
CitationAtserias, A.; Lauria, M.; Nordström, J. Narrow proofs may be maximally long. A: IEEE Conference on Computational Complexity. "IEEE 29th Conference on Computational Complexity: 11-13 June 2014, Vancouver, British Columbia, Canada: proceedings". Vancouver: Institute of Electrical and Electronics Engineers (IEEE), 2014, p. 286-297.
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder. If you wish to make any use of the work not provided for in the law, please contact: email@example.com