Abstract
Boolean nested canalizing functions (NCF) have important applications in molecular regulatory networks, engineering and computer science. In the literature, there are two sensitivities to measure the complexity of a Boolean function. One is average sensitivity, the other one is maximal sensitivity. We follow the tradition and omit the word “maximal”. In other words, in this paper, sensitivity is always maximal sensitivity. Using the past work of the authors and their coauthors on a characterization of NCF, we obtain the formula of the sensitivity of any NCF. We find that the sensitivity of any NCF is between ⌈n+22⌉ and n. Both lower and upper bounds are tight. We prove that the block sensitivity, hence the l-block sensitivity, is the same as the sensitivity for NCF. It is well known that monotone Boolean functions (MBF) also have this property. We characterize all functions which are both monotone and nested canalizing (MNCF). The closed formula of the cardinality of the set of MNCFs is also provided.
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