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$\{g\in\mathtt{CFG}(\{a,b\})\mid\mathcal{L}(g)=\{a,b\}^*\}\quad\leq\quad\{G\mid\mathcal{L}(G)=\{w\in\{a,b\}^* : |w|_{aa}\geq 1\}\}$
Reduce the universality problem on CFGs over $\{a,b\}$ to the problem of
whether a CFG generates all words over $\{a,b\}$ with at least one occurrence
of $aa$, in order to prove that such problem is not semi-decidable (not
recursively enumerable).
Authors: Carles Creus, Guillem Godoy
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