Sensitivity, block sensitivity, and certificate complexity of unate functions and read-once functions

Abstract

Sensitivity, block sensitivity, and certificate complexity are complexity measures for Boolean functions. In this paper, we prove that these three complexity measures are equal to each other if a Boolean function is a unate function or a read-once function. We also prove √n tight lower bounds for the three complexity measures of read-once functions. As an application of our results, the decision tree complexity of unate functions and read-once functions is upper bounded by the square of the sensitivity of the function. © 2014 IFIP International Federation for Information Processing.