Houjun Liu

Space Time Hierachy

I finally get to sound like I’m doing physics.

\begin{equation} L \subseteq P \subseteq \text{PSPACE} \subseteq \text{EXP} \end{equation}

by space hierarchy theorem and time hierarchy theorem, we have also that:

\begin{equation} \text{P} \subset \text{EXP} \end{equation}

and

\begin{equation} L \subset\text{PSPACE} \end{equation}

so we know that one of the subset things on top is a strict subset. There’s also a bridge \(P \subseteq \text{NP} \subseteq \text{PSPACE}\).

\(L =^{?} P\)

We believe that \(L \subset P\), but we can’t show this.

\(L =^{?} \text{NP}\)

We believe that \(L \subset \text{NP}\), but we can’t show this