# How to disprove that DTIME(f) = NSPACE(f)?

Is there an easy way (maybe by using hierarchy theorems) to disprove that $DTIME(f) = NSPACE(f)$ for any computable $f: \mathbb{N}\rightarrow\mathbb{N}$ with $f(n)\geq n$?

• Try diagonalization. Follow the proofs of the time and space hierarchy theorems. – Yuval Filmus Sep 3 '18 at 23:10