### On the number of fixed points of a Boolean transformation

#### Abstract

In [1] the authors determine the Boolean transformations F :{0, 1}^2 −> {0, 1}^2 which have two fixed points, via the semi-tensor product method.

In the present paper, using the irredundant solution of a Boolean equation in an arbitrary Boolean algebra, which we have devised in [2], we obtain two generalizations.

First we find the fixed points of a Boolean transformation F : B^2 −> B^2 in an arbitrary Boolean algebra B.

Secondly, we describe explicitly the form of the transformations F : {0, 1}^2 −> {0, 1}^2 having exactly k fixed points, for k = 0, 1, . . . , 4.

In the present paper, using the irredundant solution of a Boolean equation in an arbitrary Boolean algebra, which we have devised in [2], we obtain two generalizations.

First we find the fixed points of a Boolean transformation F : B^2 −> B^2 in an arbitrary Boolean algebra B.

Secondly, we describe explicitly the form of the transformations F : {0, 1}^2 −> {0, 1}^2 having exactly k fixed points, for k = 0, 1, . . . , 4.