This below language

$$L = \{ w \in \{a, b\}^n : \lvert w\rvert \text{ mod } 3 = 0 \}$$ where $n \geq0$.


closed as unclear what you're asking by xskxzr, Evil, Discrete lizard Oct 9 at 16:57

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    $\begingroup$ Could you design a CFG for a language where each string had length exactly three? If so, it's just a tiny modification to get what you want. $\endgroup$ – Rick Decker Oct 8 at 18:53

Since this seems very much like homework, i will give you a little Hint, taking as example a sub-case of your language:

The GFC for the string $a^3b^3$ is the following:

$S ⇒ aSb$

$aSb ⇒ aaSbb$

$aaSbb ⇒ aaaSbbb$

$aaaSbbb ⇒ aaabbb$

You can take the above as a starting point from which to adapt the grammar to your case.

  • $\begingroup$ Thank you very much $\endgroup$ – Abhimanyu Bansal Oct 27 at 7:35

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