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!


1 Answer 1


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 $O(n)+2\log n =O(n)$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.