Sensitivity and block sensitivity of nested canalyzing function

Abstract

Based on a recent characterization of nested canalyzing function (NCF), we obtain the formula of the sensitivity of any NCF. Hence we find that any sensitivity of NCF is between $\frac{n+1}{2}$ and $n$. Both lower and upper bounds are tight. We prove that the block sensitivity, hence the $l$-block sensitivity, is same to the sensitivity. It is well known that monotone function also has this property. We eventually find all the functions which are both monotone and nested canalyzing (MNCF). The cardinality of all the MNCF is also provided.