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Dec 22, 2009 at 2:35 comment added David Eppstein A simpler but similar argument: if you had a gate with three inputs u,v,w that computed the function (u ⋀ v ⋀ w) ⋁ (¬u ⋀ ¬v ⋀ ¬w) you could use it to split one variable u into two equivalent variables v and w and get around the two-occurrences-per-variable limitation.
Dec 22, 2009 at 2:34 comment added Ryan Williams Very nice observation. This suggests another question: which collections of basis gates make the problem easy, and which make the problem hard? My intuition is that the choice of basis gates should make a huge difference.
Dec 22, 2009 at 2:24 history answered David E Speyer CC BY-SA 2.5