Recognition complexity for Schaefer classes (Q1382588)

Let \(F = \{f_j(x_1,x_2,\dots,x_{k_j})\not\equiv 0\mid j\in J\}\) be a finite set of Boolean functions set in conjunctive normal form (CNF). The class of various systems of equations \[ \{f_{j_i}(x_{i1},x_{i2},\dots,x_{ik_{j_i}})\} = 1,\qquad i = \overline{1, m} \] is called the class of \(F\)-systems for any choice of the functions \(f_{j_i}\) from \(F\) with any finite number \(m\) of equations in each system and for any choice of unknown \(x_{ij}\) from the set \(X = \{x_1,x_2,\dots\}\). The problem of \(F\)-jointness is a problem of jointness recognizing an arbitrary system of equations from the class of \(F\)-systems. The set of functions \(F\) is called \(P\)-set, if there exist a polynomial algorithm solving the \(F\)-jointness problem and an \(NP\)-complete set, if the problem of \(F\)-jointness is \(NP\)-complete. The author proves that the problem of recognizing multiaffinity, bijunctiveness, weak-positiveness and weak-negativeness of a Boolean function given in CNF is \(NP\)-complete.