  Boolean functions can be represented in many ways including logical forms,
truth tables, and polynomials. Additionally, Boolean functions have different
canonical representations such as minimal disjunctive normal forms. Other
canonical representation is based on the polynomial representation of Boolean
functions where they can be written as a nested product of canalizing layers
and a polynomial that contains the noncanalizing variables. In this paper we
study the problem of identifying the canalizing layers format of Boolean
functions. First, we show that the problem of finding the canalizing layers is
NP-hard. Second, we present several algorithms for finding the canalizing
layers of a Boolean function, discuss their complexities, and compare their
performances. Third, we show applications where the computation of canalizing
layers can be used for finding a disjunctive normal form of a nested canalizing
function. Another application deals with the reverse engineering of Boolean
networks with a prescribed layering format. Finally, implementations of our
algorithms in Python and in the computer algebra system Macaulay2 are available
at https://github.com/ckadelka/BooleanCanalization.
