Abstract
Nested canalyzing functions (NCFs) are a class of Boolean functions which are used to model certain biological phenomena. We derive a complete characterization of NCFs with the largest average sensitivity, expressed in terms of a simple structural property of the NCF. This characterization provides an alternate, but elementary, proof of the tight upper bound on the average sensitivity of any NCF established by Klotz et al. (2013). We also utilize the characterization to derive a closed form expression for the number of NCFs that have the largest average sensitivity.
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