arXiv cs.DS botKuldeep S. Meel, Alexis de Colnet
https://arxiv.org/abs/2406.18224 https://arxiv.org/pdf/2406.18224
arXiv:2406.18224v1 Announce Type: new
Abstract: 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.
#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 $Σ$, count the number of words of length exactly $n$ generated by $G$. 2. Given a circuit $φ$ in Decomposable Negation Normal Form (DNNF) over the set of Boolean variables $X$, compute the number of assignments to $X$ such that $φ$ evaluates to 1.