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Context-free description for $\{ w_1aw_2aw_3 \mid w_1,w_2,w_3\in\{0,1\}^*\;\wedge\;|w_1|=|w_2|_0+|w_3|_1\;\wedge\;|w_1w_2|_{111}\geq 1 \}$
Give a context-free description for the set of words of the form $w_1aw_2aw_3$ such that
$w_1,w_2,w_3$ are constructed over the alphabet $\{0,1\}$, the size $w_1$ coincides with
the number of $0$’s of $w_2$ plus the number of $1$’s of $w_3$, and
$w_1w_2$ has at least one occurrence of $111$.
Authors: Guillem Godoy
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