Title:
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Lower bounds for DNF-refutations of a relativized weak pigeonhole principle
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Author:
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Atserias, Albert; Müller, Moritz; Oliva Valls, Sergi
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Ciències de la Computació; Universitat Politècnica de Catalunya. ALBCOM - Algorismia, Bioinformàtica, Complexitat i Mètodes Formals |
Abstract:
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The relativized weak pigeonhole principle states that if at least 2n out of n(2) 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-is an element of) for every is an element of > 0 and every sufficiently large n. By reducing it to the standard weak pigeonhole principle with 2n pigeons and n holes, we also show that this lower bound is essentially tight in that there exist DNF-refutations of size 2((log n)O(1)) even in R(log). For the lower bound proof we need to discuss the existence of unbalanced low-degree bipartite expanders satisfying a certain robustness condition. |
Abstract:
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Peer Reviewed |
Subject(s):
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-Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica -Computational complexity -Proof complexity -Bounded arithmetic -Weak pigeonhole principles -Approximate counting -Bounded-depth frege -Propositional proof systems -Resolution lower bounds -Random formulas -Complexity gap -Primes -Size -Complexitat computacional |
Rights:
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Document type:
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Article - Published version Article |
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