PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Rights accessOpen Access
The relativized weak pigeonhole principle states that if at least 2n out of n2 pigeons fly into n holes, then some hole must be doubly occupied. We prove that every DNF-refutation of the CNF encoding of this principle requires size 2((log n)3/2-ϵ) for every ε > 0 and every sufficiently large n. For its proof we need to discuss the existence of unbalanced low-degree bipartite expanders satisfying a certain robustness condition.
CitationAtserias, A.; Müller, M.; Oliva, S. Lower bounds for DNF-refutations of a relativized weak pigeonhole principle. A: IEEE Conference on Computational Complexity. "2013 IEEE Conference on Computational Complexity, CCC 2013: 5-7 June 2013 Palo Alto, California, USA: proceedings". Palo Alto, California: Institute of Electrical and Electronics Engineers (IEEE), 2013, p. 109-120.
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