It is known that the language $\{a^nb^nc^n|n\geq0\}$ is not context-free (we can prove it using the pumping lemma, as shown here: Is $a^n b^n c^n$ context-free?). Yet, this answer claims it has found a context-free grammar for this language. My question is, is it possible to find a context free grammar for a not context-free language?
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2The CFG is not given for $L = {a^nb^nc^n\mid n\geqslant 0}$ in the post you quote, but for $a^b^c^*\setminus L$ which is context-free. – Nathaniel Apr 07 '22 at 23:05
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No. Every context-free grammar generates a context-free language. If you can find a context-free grammar for a language, then the language is context-free.
That assumes the claimed grammar is correct. People claim all sorts of things on the Internet. I wouldn't believe it until you have verified or proven it correct. In this particular case, the answer was incorrect and the grammar doesn't work. I left a comment explaining, and indeed, another answer already responded to that erroneous claim.
D.W.
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