Thursday, January 22, 2009

Lecture 4

The topics covered in Lecture 4 were: Adleman's Theorem, $BPP \in P/poly$; Poly-time hierarchy; Min-Circuit; Infinite Hierarchy Assumption, Collapse Lemma; $PSPACE =$ Alternating Poly Time statement; Oracles, $\Sigma_2 = NP^{NP}$, etc; Sipser-Gacs-Lautemann Theorem, $BPP \in \Sigma_2$; Karp-Lipton(-Sipser) Theorem, $NP \subseteq P/poly \Rightarrow PH = \Sigma_2$; Valiant-Vazirani Theorem statement, UniqueSat $\in P \Rightarrow NP = RP$.

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