On the complexity of cutting-plane proofs
Discrete Applied Mathematics
A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
On the Chvátal rank of polytopes in the 0/1 cube
Discrete Applied Mathematics
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
Bounds on the Chvátal Rank of Polytopes in the 0/1-Cube
Combinatorica
Rank complexity gap for Lovász-Schrijver and Sherali-Adams proof systems
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the Asymptotic Nullstellensatz and Polynomial Calculus Proof Complexity
LICS '08 Proceedings of the 2008 23rd Annual IEEE Symposium on Logic in Computer Science
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We introduce the parameter cutwidth for the Cutting Planes (CP ) system of Gomory and Chvátal. We provide linear lower bounds on cutwidth for two simple polytopes. Considering CP as a propositional refutation system, one can see that the cutwidth of a CNF contradiction F is always bound above by the Resolution width of F . We provide an example proving that the converse fails: there is an F which has constant cutwidth, but has Resolution width ***(n ). Following a standard method for converting an FO sentence *** , without finite models, into a sequence of CNFs, F *** ,n , we provide a classification theorem for CP based on the sum cutwidth plus rank. Specifically, the cutwidth+rank of F *** ,n is bound by a constant c (depending on *** only) iff *** has no (infinite) models. This result may be seen as a relative of various gap theorems extant in the literature.