Explicit lower bound of 4.5n - o(n) for boolena circuits

Authors:
Oded Lachish;Ran Raz
Affiliations:
Department of Computer Science, Weizmann Institute, Rehovot 76100, Israel;Department of Computer Science, Weizmann Institute, Rehovot 76100, Israel
Venue:
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Year:
2001

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Abstract

We prove a lower bound of 4.5n - o(n) for the circuit complexity of an explicit Boolean function (that is, a function constructible in deterministic polynomial time), over the basis U_2. That is, we obtain a lower bound of 4.5n - 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 Strongly-Two-Dependent Boolean function.