Exploiting Independent Subformulas: A Faster Approximation Scheme for #k-SAT

We present an improvement on Thurley’s recent randomized approximation scheme for #k-SAT where the task is to count the number of satisfying truth assignments of a Boolean function {\Phi} given as an n-variable k-CNF. We introduce a novel way to identify independent substructures of {\Phi} and can therefore reduce the size of the search space considerably. Our randomized algorithm works for any k. For #3-SAT, it runs in time O(\epsilon^{-2}*1.51426^n), for #4-SAT, it runs in time O(\epsilon^{-2}*1.60816^n), with error bound \epsilon.