We introduce the concept of Sheffer operation in ortholattices and, more generally, in lattices with antitone involution. By using this, all the fundamental operations of an ortholattice or a lattice with antitone involution are term functions built up from the Sheffer operation. We list axioms characterizing the Sheffer operation in these lattices.
A De Morgan quasilattice is an algebra satisfying hyperidentities of the variety of De Morgan algebras (lattices). In this paper we give a functional representation of the free n-generated De Morgan quasilattice with two binary and one unary operations. Namely, we define the concept of super-De Morgan function and prove that the free De Morgan quasilattice with two binary and one unary operations on nfree generators is isomorphic to the De Morgan quasilattice of super-De Morgan functions of nvariables....
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 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...
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.