AP06_1.vp 1 Introduction The procedure in the design of logical structural models with multiplexors might seem to be complete. It appears, however, that the Artjuchov-Shalyto extension of the Boolean function, which models the performance of a multiplexor, leads to its mere “setting”, and the generalised model of the multiplexor performance makes it possible to design structural models with multiplexors according to the disjoint decomposition of the given Boolean function. 2 Boolean function Let the Boolean function f x x x ym m:{ , } { , }: , , ,0 1 0 1 1 2� � � be given. If we denote the set { }xi i m �1 of the function f argu- ments by the symbol X, we can write f(X) instead of f(x1, x2, …, xm). Let us also write f(xi � �i) instead of f(x1, x2, …, xi�1, �i, xi�1, …, xm), where �i � {0, 1}. We require the function f(X)to be minimal with respect to the number of arguments, i.e., not to contain fictive arguments; the argument xi is called fictive if f(xi � 0) � f(xi � 1). The term Hamming weight wH of the function f – wH f – denotes the value of the arithmetic expression w f X fH m m m ( ) ( , , , ) , , , { , } � � � � � � � � � � � 1 2 0 11 2 Let x x x� � � � � � �� � � 0 1 ; each Boolean function f(X) can be expressed by means of a canonic normal disjunctive formula – cndf f(X) f X x x x f m m m m m( ) ( , , , ) , , , { , } � � � � � �� � � � � � � � � 1 2 1 2 0 1 1 2 1 2� . Then, if w fH m 2 2 or w fH m� 2 2, or if w fH m� 2 2, it is preferable to write down the respective cndf f(X) or cndf f X( ), or to apply the Artjuchov-Shalyto extension of the func- tion f(X) [1] f X x x f x x f x f X x x f x x f x i i i i i i i i i ( ) ( ) ( ) ( ) ( ) ( � � � � � � � � � 0 1 0 i �1) the validity of which can be easily confirmed by supplying 0 or 1 for xi. Let a dichotomy {X1, X0}be given on a set of X arguments x1, x2, , xm without loss of generality, such that X1 � {x1, x2, …, xn} and X0 � {xn�1, xn�2, …, xm}, where n