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As said in the title, i am quite curious wether NSPACE(2^(O(n)) equals NSPACE(n^2 * 2^(O(n))

I am aware of the fact, that NSPACE(k * 2^O(n)) equals NSPACE(2^O(n)) due to linear space reduction (i.e. some sort of super character representing k characters)

But since neighter n nor n^2 is linear, we cant use this here.

Thanks for your advise!

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Yes. Clearly NSPACE($2^{O(n)}$) $\subseteq $ NSPACE($n^2 \cdot 2^{O(n)}$).

To show that NSPACE($2^{O(n)}$) $\supseteq $ NSPACE($n^2 \cdot 2^{O(n)}$) it suffices to notice that $n^2 \cdot 2^{O(n)} = 2^{O(n) + 2\log n}$ and $O(n)+2\log n =O(n)$.

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