15-855: Intensive Intro to Computational Complexity: Lecture 4

Thursday, January 22, 2009

The topics covered in Lecture 4 were: Adleman's Theorem,

B P P \in P / p o l y

; Poly-time hierarchy; Min-Circuit; Infinite Hierarchy Assumption, Collapse Lemma;

P S P A C E =

Alternating Poly Time statement; Oracles,

Σ_{2} = N P^{N P}

, etc; Sipser-Gacs-Lautemann Theorem,

B P P \in Σ_{2}

; Karp-Lipton(-Sipser) Theorem,

N P \subseteq P / p o l y \Rightarrow P H = Σ_{2}

; Valiant-Vazirani Theorem statement, UniqueSat

\in P \Rightarrow N P = R P