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The (block-)composition of two Boolean functions $$f : \{0, 1\}^{m} \rightarrow \{0, 1\}, g : \{0, 1\}^{n} \rightarrow \{0, 1\}$$ f : { 0 , 1 } m → { 0 , 1 } , g : { 0 , 1 } n → { 0 , 1 } is the function $$f \diamond g$$ f ⋄ g that takes as inputs m strings $$x_{1}, \ldots , x_{m} \in \{0, 1\}^{n}$$ x 1 , … , x m ∈ { 0 , 1 } n and computes $$(f \diamond...
One of the major challenges of the research in circuit complexity is proving super-polynomial lower bounds for de Morgan formulas. Karchmer et al. (Comput Complex 5(3/4):191–204, 1995b) suggested to approach this problem by proving that formula complexity behaves “as expected” with respect to the composition of functions $${f\diamond g}$$ f⋄g . They showed that this conjecture, if proved, would imply...
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