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.
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Meel et al. (2024) studied this question.
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