This site uses cookies only for the purpose of identifying user sessions.
This is required to properly register actions.

##
Exercise
_{‹}11:

Context-free description for $\{ w_1aw_2aw_3 \mid w_1,w_2,w_3\in\{0,1\}^*\;\wedge\;|w_1|=|w_3|\;\wedge\;\mathtt{value}_2(w_1w_3)\in\dot{12}\;\wedge\;w_2\in\{0^n1^n\mid n\geq 0\} \}$

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 sizes of $w_1$ and $w_3$ coincide,
$w_1w_3$ represent a multiple of $12$ in binary (in particular, the empty word represents $0$, which is multiple of $12$),
and $w_2$ is a sequence of $0$’s followed by
a sequence of $1$’s where the number $0$’s and $1$’s coincide.

Authors: Guillem Godoy
/

Documentation: