Rank complexity gap for Lovász-Schrijver and Sherali-Adams proof systems (2012)
Journal Article
Dantchev, S., & Martin, B. (2013). Rank complexity gap for Lovász-Schrijver and Sherali-Adams proof systems. Computational Complexity, 22(1), 191-213. https://doi.org/10.1007/s00037-012-0049-1

We prove a dichotomy theorem for the rank of propositional contradictions, uniformly generated from first-order sentences, in both the Lovász-Schrijver (LS) and Sherali-Adams (SA) refutation systems. More precisely, we first show that the proposition... Read More about Rank complexity gap for Lovász-Schrijver and Sherali-Adams proof systems.

Cutting Planes and the Parameter Cutwidth (2012)
Journal Article
Dantchev, S., & Martin, B. (2012). Cutting Planes and the Parameter Cutwidth. Theory of Computing Systems, 51(1), 50-64. https://doi.org/10.1007/s00224-011-9373-0

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... Read More about Cutting Planes and the Parameter Cutwidth.