A major consideration we had in writing this survey was to make it accessible to mathematicians as well as to computer scientists, since expander graphs, the protagonists of our story, come up in… Expand

We present a new method for proving rank lower bounds for Cutting Planes (CP) and several procedures based on Lovász and Schrijver (LS), when viewed as proof systems for unsatisfiability.Expand

What is the maximum number of edges in a bipartite graph of girth g whose left and right sides are of size nL, nR? We generalize the known results for g = 6, 8 to an arbitrary girth.

The (k,s)-SAT problem is the satisfiability problem restricted to instances where each clause has exactly k literals and every variable occurs at most s times.Expand

A non-backtracking walk on a graph, H, is a directed path of directed edges of H such that no edge is the inverse of its preceding edge. Non-backtracking walks of a given length can be counted using… Expand

We present a new method for proving rank lower bounds for Cutting Planes and Lovasz-Schrijver proofs for several prominent CNF examples, including random kCNF formulas and the Tseitin graph formulas.Expand