Before revision:  The first result is a polynomial normal form representation for discrete functionsthat provides a partition of the inputs of the function into canalizing and non-canalizing variables and, within the canalizing ones, we categorize the input variables into layers of canalization.
After revision:  The first result is a polynomial normal form based on the canalizing properties of regulatory functions. This polynomial normal form provides a partition of the inputs of the function into canalizing and non-canalizing variables and, within the canalizing ones, we categorize the input variables into layers of canalization.