Check whether the following language is context-free. If yes, a suitable grammar should be given; if no, the pumping lemma should be used as a tool.

$$L=\{a^ib^jc^k \mid i, j, k \in N \text{ and } i <k<j\} $$

Can I choose (since N includes 0)

$$ L=\{b^jc^k \mid j,k >= 1 \text{ and } j > k\} $$

and provide a grammar for that language, and thus say L is indeed context-free? If L is not context-free, how could I prove it using the Pumping Lemma?

  • $\begingroup$ Does this answer your question? $\endgroup$
    – Nathaniel
    Jun 4 at 12:48
  • $\begingroup$ Also, if $L\subset L'$ and $L$ is context-free, that does not mean that $L'$ is context-free, but that is the reasoning you are trying to do. $\endgroup$
    – Nathaniel
    Jun 4 at 12:50