Higher lower bounds on monotone size

  title={Higher lower bounds on monotone size},
  author={Danny Harnik and Ran Raz},
We prove a lower bound of 2 f l ( ( ~ ) ~ ) o n t h e m o n o tone size of an explicit function in monotone-Af:P (where n is the number of input variables). This is higher than any previous lower bound on the monotone size of a function. The previous best being a lower bound of about 2 ~('~1⁄4) for Andreev 's function, proved in [A1Bo87]. Our lower bound is proved by the symmetr ic version of Razborov 's method of approximations. However, we present this method in a new and simpler way: Rather… CONTINUE READING