An Explicit Lower Bound of 5n - o(n) for Boolean Circuits

We prove a lower bound of 5n − o(n) for the circuit complexity of an explicit (constructible in deterministic polynomial time) Boolean function , over the basis U2. That is, we obtain a lower bound of 5n−o(n) for the number of {and, or} gates needed to compute a certain Boolean function, over the basis {and, or, not} (where the not gates are not counted). Our proof is based on a new combinatorial property of Boolean functions, called Strongly-Two-Dependence, a notion that may be interesting in its own right. Our lower bound applies to any StronglyTwo-Dependent Boolean function.