So I have a language: $$ L = \{a^{n^2} \mid n > 0\} $$ I need to prove that this language isn't context free using the pumping lemma. I have a vague thought process as to how to do the proof but I'm sort of doubting it's validity.

So I take a pumping length $p$ such that a word $a^{p^2}$ can be split into 5 parts $uvxyz$. I need to assume that $L$ is context free and run through some cases and check if the word violates the pumping lemma or if it doesn't violate the pumping lemma but isn't in the language definition.

I know the concept of proving languages aren't context free and the pumping lemma but I'm very stuck applying it to this particular language.

What do I do?

Thanks for your help

So I have a language: $$ L = \{a^{n^2} \mid n > 0\} $$ I need to prove that this language isn't context-free using the pumping lemma. I have a vague thought process as to how to do the proof but I'm sort of doubting its validity.

So I take a pumping length $p$ such that a word $a^{p^2}$ can be split into 5 parts $uvxyz$. I need to assume that $L$ is context-free and run through some cases and check if the word violates the pumping lemma or if it doesn't violate the pumping lemma but isn't in the language definition.

I know the concept of proving languages aren't context free and the pumping lemma but I'm very stuck applying it to this particular language.

What do I do?

So I have a language:

L = {a^n^2 | n is a natural number} (a^n^2 means a to the power of n squared)

I need to prove that this language isn't context free using the pumping lemma. I have a vague thought process as to how to do the proof but I'm sort of doubting it's validity.

So I take a pumping length p such that a word a^p^2 can be split into 5 parts uvxyz. I need to assume that L is context free and run through some cases and check if the word violates the pumping lemma or if it doesn't violate the pumping lemma but isn't in the language definition.

I know the concept of proving languages aren't context free and the pumping lemma but I'm very stuck applying it to this particular language.

What do I do?

Thanks for your help

So I have a language: $$ L = \{a^{n^2} \mid n > 0\} $$ I need to prove that this language isn't context free using the pumping lemma. I have a vague thought process as to how to do the proof but I'm sort of doubting it's validity.

So I take a pumping length $p$ such that a word $a^{p^2}$ can be split into 5 parts $uvxyz$. I need to assume that $L$ is context free and run through some cases and check if the word violates the pumping lemma or if it doesn't violate the pumping lemma but isn't in the language definition.

I know the concept of proving languages aren't context free and the pumping lemma but I'm very stuck applying it to this particular language.

What do I do?

Thanks for your help