Narrow proofs may be maximally long
Tipo de documentoTexto en actas de congreso
Fecha de publicación2014
EditorInstitute of Electrical and Electronics Engineers (IEEE)
Condiciones de accesoAcceso abierto
Proyecto de la Comisión EuropeaUTHOTP - Understanding the Hardness of Theorem Proving (EC-FP7-279611)
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.
CitaciónAtserias, A.; Lauria, M.; Nordström, J. Narrow proofs may be maximally long. A: IEEE Conference on Computational Complexity. "IEEE 29th Conference on Computational Complexity: 11-13 June 2014, Vancouver, British Columbia, Canada: proceedings". Vancouver: Institute of Electrical and Electronics Engineers (IEEE), 2014, p. 286-297.
Versión del editorhttp://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6875497