Thursday, February 5, 2009

Lecture 8

Today we proved the following five theorems:

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

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

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

4. TQBF is $PSPACE$-complete.

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

Here $s(n) \geq \log n$ 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 :)

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