Lecture 8 : AC 0 Circuit Size of SUB ( G )
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چکیده
We say θ is strict if ∆θ(H) > 0 for all ∅ ⊂ H ⊂ G. • Xθ is the random subgraph of G↑n where, independently for each {v(i), w(j)} ∈ E(G↑n), P[ {v, w} ∈ E(Xθ) ] = n−θ({v,w}). We have E[ subH(Xθ) ] = n ∆θ(H). If θ is strict, then subG(Xθ) is asymptotically Poisson(1) and subH(Xθ) is highly concentration around its mean for all ∅ ⊂ H ⊂ G. Convention. In the context of lower bounds for SUB(G), the adjective “AC0” refers to circuits of depth o( logn log logn). (Our upper bounds will only require constant depth: O(|E(G)|) in terms of G.) Over the next two lectures, we will present results of Li, Razborov and Rossman (2014) that
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Lecture 9 : AC 0 Circuit Size of SUB ( G ) , Continued
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