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 single-exponential 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.