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Título:
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Lower bounds for DNF-refutations of a relativized weak pigeonhole principle
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Autor/a:
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Atserias, Albert; Müller, Moritz; Oliva Valls, Sergi
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Otros autores:
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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 |
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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. |
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Abstract:
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Peer Reviewed |
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Materia(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 |
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Derechos:
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Tipo de documento:
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Artículo - Versión publicada
Artículo |
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