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Valiant [12] showed that the clique function is structurally different than the majority function by establishing the following "switching lemma ~ : Any function f whose set of prime implicants is a large enough subset of the set of cliques (and thus requiring big ~2-circuits), has a large set of prime clauses (i.e., big II2-circuits). As a corollary, an… (More)

We show that the complexity classes AC0 and NC' consist exactly of, respectively, constant and O(log n) width polynomial-size Boolean formulas.

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