# Can we replace deterministic part of alternative turing machine with some other equivalent machines?

I'm sorry if it is a low level question but I am so confusing.

If $DTime(n)\subseteq \Sigma_2Time(n^{0.2})$ then $DTime(n) \subseteq \Sigma_2DTime(n^{0.2})$

Is this true that $\Sigma_2DTime(n^{0.2})\subseteq\Sigma_2\Sigma_2Time((n^{0.2})^{0.2})=\Sigma_4Time(n^{0.04})$

I picked up DTime in alternative machine and replaced it with $DTime(n)\subseteq \Sigma_2Time(n^{0.2})$ and replacing n with $n^{0.2}$.

I think you need to work on what $(0.2)^2$ is before you go any further.
• I'm sorry I think it is 0.04 in the question it is $(n^{0.2})^{0.2}$.If we suppose $DTime(n) \subseteq \Sigma_2Time(n^{0.2})$ then $DTime(n^{0.2}) \subseteq \Sigma_2Time(n^{0.04})$ I want to calculate $\Sigma_2DTime(n^{0.2})$ so I picked $DTime(n^{0.2})$ and replaced with $\Sigma_2Time(n^{0.04})$ and I recived to $\Sigma_2DTime(n^{0.2})\subseteq\Sigma_2\Sigma_2Time(n^{0.04})=\Sigma_4Time(n^{0.04})$. I want to know is this correct? thanks alot. – Song Aug 11 '18 at 6:09