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During a class, we was asked how to prove that a language L is strictly context-sensitive. In particular, we have to prove that

$L = \{a^nb^nc^n \mid n > 0\}$

Could you help me to find the answer providing a detailed solution?

My approach:

I know that a language is strictly of type $n$ if there isn't a type-$j$-grammar ($j > n$) that can generate it.

So i wonder if i can apply the Pumping Lemma for Context Free Languages to prove that.

Jack
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