#CFG and #DNNF admit FPRAS

We provide the first fully polynomial-time randomized approximation scheme for the following two counting problems:1.Given a Context-Free Grammar $G$ over alphabet $\Sigma$, count the number of words of length exactly $n$ generated by $G$2.Given a circuit $\varphi$ in Decomposable Negation Normal Form (DNNF) over the set of Boolean variables $X$, compute the number of assignments to $X$ such that $\varphi$ evaluates to 1.