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CS254 Lecture 4 – The Polynomial Hierarchy
Today we show how to reduce the error probability of probabilistic algorithms, prove Adleman’s theorem that polynomial time probabilistic algorithms can be simulated by polynomial size circuits, and...
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CS254 Lecture 5 – The Polynomial Hierarchy
Last revised 4/29/2010 In this lecture, we first continue to talk about polynomial hierarchy. Then we prove the Gács-Sipser-Lautemann theorem that BPP is contained in the second level of the...
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CS245 Lecture 6 – Karp-Lipton
In this lecture we prove the Karp-Lipton theorem that if all NP problems have polynomial size circuits then the polynomial hierarchy collapses. A nice application is a theorem of Kannan, showing that,...
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