Boolean Relations Research Articles

Ordering of Implicants

Correspondence between logical relations of Boolean function implicants and numerical relations between identifiers

Graphs and Matrices

Graphs and Matrices

On the graphs and asymptotic forms of finite boolean relation matrices and stochastic matrices

On the graphs and asymptotic forms of finite boolean relation matrices and stochastic matrices

Remarks about a closure algebra in which closed elements are open

1. C-5 algebras. A C-5 algebra is defined as follows: DEFINITION 1.1. An ordered quadruple a= (A, *, -, C) is said to be a C-5 algebra if the following conditions are satisfied: (i)(A, *,-) is a Boolean algebra. (We shall use + as the Boolean operation of addition; < as the Boolean relation of less than or equal to; 0 and 1 as the zero and unit elements of the Boolean algebra.) (ii) C is a unary function from A to A. (iii) x < Cx for all x in A. (iv) CCx= Cx for all x in A. (v) C(x+y) = Cx+ Cy for all x and y in A. (vi) CO = 0. (vii) -C-Cx=Cx for all x in A. REMARK. The algebra a of 1.1 is said to be a closure algebra if it satisfies (i)-(vi).

On transitive Boolean relations

On transitive Boolean relations