Lecture 8

Today we proved the following five theorems:

1. $NSPACE\left(s\right(n\left)\right)\subseteq DTIME\left(2^{O\left(s\right(n\left)\right)}\right).$

2. ST-Connectivity is $NL$-complete.

3. Savitch's Theorem: $NSPACE\left(s\right(n\left)\right)\subseteq DSPACE\left(s\right(n{)}^2)$.

4. TQBF is $PSPACE$-complete.

5. Immerman-Szelepcsényi Theorem: $NSPACE\left(s\right(n\left)\right)\subseteq coNSPACE\left(s\right(n\left)\right)$.

Here $s\left(n\right)\ge \log n$ is a space-constructible bound. (I believe that for most of these, if you want to get really really technical, you can even drop space-constructibility :)