Investigation of some subclasses of multiaffine, bijunctive, weakly positive and weakly negative Boolean functions

Sets of multiaffine (denoted by $A$), bijunctive ($2$-CNF, $Bi$), weakly positive (or anti-Horn, $WP$) and weakly negative (or Horn, $WN$) Boolean functions generate classes of polynomially solvable systems of equations. We investigate functional classes $A\cap B$, $Bi\cap B$, where $B$ is the set of bent functions. Sets of possible values of algebraic nonlinearity degree of functions from $A$, $Bi$, $WP$, $WN$ are described. Problems of construction of functions from classes $WP$, $WN$ by means of functions of smaller number of variables are considered.