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# [Solved]: Build a context-free grammar for a context-free language

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Problem Detail:

A context-free language is defined by its description:

$L=(a^{2k} \space b^n \space c^{2n} \mid k \geq 0, \space n > 0)$

For example:

$bcc, aabcc, aabbcccc, bbcccc$

How to build a context-free grammar for this context-free language?

I suppose that the order for generating any chain in this problem matters: 'b' will always stand after 'a' and 'c' - after 'b'. Is it so?

My attempts leaded to this solution:

$S \rightarrow aaAbcc \mid bAcc \mid aabAcc$

$A \rightarrow aa \mid bcc \mid λ$

Please correct me if I'm wrong or better offer your solution to this problem.

###### Asked By : Happy Torturer

$S \rightarrow EG$ , $E \rightarrow aO \mid λ$ , $O \rightarrow aE$ , $F \rightarrow bFcc \mid λ$, $G \rightarrow bFcc$ . I am assuming $λ$ stands for empty string.

Better one:

$S \rightarrow EF$ , $E \rightarrow aO \mid λ$ , $O \rightarrow aE$ , $F \rightarrow bFcc \mid bcc$.