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Narrow proofs may be maximally long
Atserias, Albert; Lauria, Massimo; Nordström, Jakob
Universitat Politècnica de Catalunya. Departament de Ciències de la Computació; Universitat Politècnica de Catalunya. ALBCOM - Algorismia, Bioinformàtica, Complexitat i Mètodes Formals
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.
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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Institute of Electrical and Electronics Engineers (IEEE)
         

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