We study the Chvátal rank of polytopes as a complexity measure of unsatisfiable sets of clauses. Our first result establishes a connection between the Chvátal rank and the minimum refutation length in the cutting planes proof system. The result implies that length lower bounds for cutting planes, or even for tree-like cutting planes, imply rank lower bounds. We also show that the converse impli...

We present a new method for proving rank lower bounds for Cutting Planes (CP) and several procedures based on lifting due to Lovász and Schrijver (LS), when viewed as proof systems for unsatisfiability. We apply this method to obtain the following new results: First, we prove near-optimal rank bounds for Cutting Planes and LovászSchrijver proofs for several prominent unsatisfiable CNF examples,...

In recent years, there has been an increasing interest in extending stream processing engines with rule-based temporal reasoning capabilities. To ensure correctness, such systems must be able to output results over the partial data received so far as if entire (infinite) had available; furthermore, these streamed out soon relevant is received, thus incurring minimum possible delay; finally, due...

An advantage of the supremum log-rank over the standard log-rank statistic is an increased sensitivity to a wider variety of stochastic ordering alternatives. In this article, we develop a formula for sample size computation for studies utilizing the supremum log-rank statistic. The idea is to base power on the proportional hazards alternative, so that the supremum log rank will have the same p...

This paper develops a new method for studying the cohomology of orthogonal flag varieties. Restriction varieties are subvarieties of orthogonal flag varieties defined by rank conditions with respect to (not necessarily isotropic) flags. They interpolate between Schubert varieties in orthogonal flag varieties and the restrictions of general Schubert varieties in ordinary flag varieties. We give ...