Título:
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Narrow proofs may be maximally long
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Autor/a:
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Atserias, Albert; Lauria, Massimo; Nordström, Jakob
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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 |
Abstract:
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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. |
Materia(s):
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-Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica -Computational complexity -Degree -Lasserre -Length -PCR -Polynomial calculus -Proof complexity -Rank -Resolution -Sherali-Adams -Size -Width -Complexitat computacional |
Derechos:
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Tipo de documento:
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Artículo - Versión presentada Objeto de conferencia |
Editor:
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Institute of Electrical and Electronics Engineers (IEEE)
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