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Consider the combinational complexity L(f) of Boolean functions over the basis Ω &equil; {f¦ f:{0,1}2 → {0,1}}. A new Method for proving linear lower bounds of size 2n is presented. Combining it with methods presented in [12] and [15], we establish for a special sequence of functions fn:{0,1}n → {0,1}: 2.5n ≤ L(f) &le 6n. Also a trade-off result between circuit complexity and formula size is derived.

A 2.5 n-lower bound on the combinational complexity of Boolean functions