Better Algorithms for Satisfiability Problems for Formulas of Bounded Rank-width

We provide a parameterized polynomial algorithm for the propositional model counting problem #SAT, the runtime of which is single-exponential in the rank-width of a formula. Previously, analogous algorithms have been known – e.g. [Fischer, Makowsky, and Ravve] – with a singleexponential dependency on the clique-width of a formula. Our algorithm thus presents an exponential runtime improvement (since clique-width reaches up to exponentially higher values than rank-width), and can be of practical interest for small values of rank-width. We also provide an algorithm for the Max-SAT problem along the same lines.