---
title: "Space Time Hierachy"
source: https://www.jemoka.com/posts/kbhspace_time_hierachy/
---

I finally get to sound like I&rsquo;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&rsquo;s also a bridge \(P \subseteq \text{NP} \subseteq \text{PSPACE}\).
\(L =^{?} P\) We believe that \(L \subset P\), but we can&rsquo;t show this.
\(L =^{?} \text{NP}\) We believe that \(L \subset \text{NP}\), but we can&rsquo;t show this
