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This is #P hard via counting solution to monotone DNF formula. Let $\phi(x_1,...x_n)$ be monotone DNF formula on $n$ variables. We are trying to find regular language $L$ over alphabet $\{0,1\}$ with all words of length $n$ and the words in $L$ are in one to one correspondence with the satisfying assignment of $\phi$. Variable $x_i$ in $\phi$ corresponds to $...

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