Exercise 20:

{gCFG({a,b})L(g)={a,b}}{GL(G)={w{a,b}:waa1}}\{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}\{a,b\} to the problem of whether a CFG generates all words over {a,b}\{a,b\} with at least one occurrence of aaaa, in order to prove that such problem is not semi-decidable (not recursively enumerable).
Authors: Carles Creus, Guillem Godoy / Documentation:
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