1 research outputs found
Symmetry Properties of Nested Canalyzing Functions
Many researchers have studied symmetry properties of various Boolean
functions. A class of Boolean functions, called nested canalyzing functions
(NCFs), has been used to model certain biological phenomena. We identify some
interesting relationships between NCFs, symmetric Boolean functions and a
generalization of symmetric Boolean functions, which we call -symmetric
functions (where is the symmetry level). Using a normalized representation
for NCFs, we develop a characterization of when two variables of an NCF are
symmetric. Using this characterization, we show that the symmetry level of an
NCF can be easily computed given a standard representation of . We also
present an algorithm for testing whether a given -symmetric function is an
NCF. Further, we show that for any NCF with variables, the notion of
strong asymmetry considered in the literature is equivalent to the property
that is -symmetric. We use this result to derive a closed form
expression for the number of -variable Boolean functions that are NCFs and
strongly asymmetric. We also identify all the Boolean functions that are NCFs
and symmetric.Comment: 17 page