The Formulas of the General Reproductive Solution of an Equation in Boolean Ring with Unit
The Rings Which Can Be Recovered by Means of the Difference
It is well known that to every Boolean ring can be assigned a Boolean algebra whose operations are term operations of . Then a symmetric difference of together with the meet operation recover the original ring operations of . The aim of this paper is to show for what a ring a similar construction is possible. Of course, we do not construct a Boolean algebra but only so-called lattice-like structure which was introduced and treated by the authors in a previous paper. In particular, we reached...
The spectral test of the Boolean function linearity
The paper discusses the problem of recognizing the Boolean function linearity. A spectral method of the analysis of Boolean functions using the Walsh transform is described. Linearity and nonlinearity play important roles in the design of digital circuits. The analysis of the distribution of spectral coefficients allows us to determine various combinatorial properties of Boolean functions, such as redundancy, monotonicity, self-duality, correcting capability, etc., which seems more difficult be...
Three generators for minimal writing-space computations
Three generators for minimal writing-space computations
We construct, for each integer n, three functions from {0,1}n to {0,1} such that any boolean mapping from {0,1}n to {0,1}n can be computed with a finite sequence of assignations only using the n input variables and those three functions.
Triangular solutions of Boolean equations.