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Title:
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Narrow proofs may be maximally long
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Author:
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Atserias, Albert; Lauria, Massimo; Nordström, Jakob
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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 |
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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. |
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Subject(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 |
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Rights:
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Document type:
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Article - Submitted version
Conference Object |
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Published by:
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Institute of Electrical and Electronics Engineers (IEEE)
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