Illustration of initial terms of A058759. We wish to realize the Boolean function f(X_1, ..., X_n) with a two-terminal network using AND's and OR's applied to the variables X_1, X_1', ..., X_n, X_n'. What we count is the total number of times the variables X_1, X_1', ..., X_n, X_n' are used. Conventions: ------------ o------o means 0 or FALSE or CLOSED o- -o means 1 or TRUE or OPEN prime means "NOT" o--- X --- Y ---o is X + Y = X OR Y X / \ o--o o--o is XY = X AND Y \ / Y -------------------------------------------- For n=1 the worst case is f = X, circuit is o---- X ----o requiring 1 variable. -------------------------------------------- For n=2 the worst case is f = X XOR Y, circuit is X X' / \ / \ o--o o o---o \ / \ / Y' Y requiring 4 uses of the variables -------------------------------------------- For n=3 the worst is X XOR Y XOR Z, circuit is o-- Y --o / \ / \ X Y' / Z / \ / \ o-o \ o-o \ / \ / X' Y' \ Z' \ / \ / o-- Y --o requiring 8 uses of the variables. --------------------------------------------