In 1996, Fredman and Khachiyan [J. Algorithms 21 (1996) 618–628] presented a remarkable algorithm for the problem of checking the duality of a pair of monotone Boolean expressions in disjunctive normal form. Their algorithm runs in no(logn) time, thus giving evidence that the problem lies in an intermediate class between P and co-NP. In this paper we show that a modified version of their algori...

We present a new measure, CNF-tree-width (CNFtw), for bounding the complexity of weighted model counting and related #P-hard problems. CNF-tw dominates known measures such as the dtree width and the treewidth of the CNF primal and incidence graphs. We present a novel approach that utilizes the junction-tree structure in order to decompose the formula. We also characterize a new class of CNFs wh...

We provide a characterization of Horn cores for formulas in conjunctive normal form (CNF) and, based on it, a novel algorithm for computing Horn cores of disjunctions of Horn CNFs that has appealing properties (e.g., it is polynomial for a bounded disjunction). Furthermore, we show that recognizing the Horn envelope of a disjunction of two Horn CNFs is intractable, and that computing a compact ...