A 2.5n lower bound on the monotone network complexity of T3n

Abstract

The k-th threshold function, T k n , is defined as: $$T_k^n \left( {x_1 ,...,x_n } \right) = \left\{ \begin{gathered} 1 if \sum\limits_{i = 1}^n {x_i \geqq k} \hfill \\ 0 otherwise \hfill \\ \end{gathered} \right.$$ where x ie{0,1} and the summation is arithmetic. We prove that any monotone network computing T 3/n(x 1,...,x n) contains at least 2.5n-5.5 gates.