A basis of the conjunctively polynomial-like Boolean functions.
A Functional Approach to the Theory of Prime Implicants
A note on indecomposability of Boolean matrices
A selection property of the boolean -calculus and some of its applications
A solution of Dedekind's problem on the number of isotone Boolean functions.
Aggregation for Quality Management
All General Reproductive Solutions of Boolean Equations
All General Solutions of Finite Equations
Boolean functions represented by random formulas
Boolean transformations with unique fixed points
Characterizations of certain general and reproductive solutions of arbitrary equations
Conjunctively polynomial-like Boolean functions.
Didactical note: probabilistic conditionality in a Boolean algebra.
This note deals with two logical topics and concerns Boolean Algebras from an elementary point of view. First we consider the class of operations on a Boolean Algebra that can be used for modelling If-then propositions. These operations, or Conditionals, are characterized under the hypothesis that they only obey to the Modus Ponens-Inequality, and it is shown that only six of them are boolean two-place functions. Is the Conditional Probability the Probability of a Conditional? This problem will...
Efficient calculation of the Reed-Muller form by means of the Walsh transform
The paper describes a spectral method for combinational logic synthesis using the Walsh transform and the Reed-Muller form. A new algorithm is presented that allows us to obtain the mixed polarity Reed-Muller expansion of Boolean functions. The most popular minimisation (sub-minimisation) criterion of the Reed-Muller form is obtained by the exhaustive search of all the polarity vectors. This paper presents a non-exhaustive method for Reed-Muller expansions. The new method allows us to build the...
Essential Arity Gap of Boolean Functions
In this paper we investigate the Boolean functions with maximum essential arity gap. Additionally we propose a simpler proof of an important theorem proved by M. Couceiro and E. Lehtonen in [3]. They use Zhegalkin’s polynomials as normal forms for Boolean functions and describe the functions with essential arity gap equals 2. We use to instead Full Conjunctive Normal Forms of these polynomials which allows us to simplify the proofs and to obtain several combinatorial results concerning the Boolean functions...
Existence of Periodic Solutions for Nonlinear Neutral Dynamic Equations with Functional Delay on a Time Scale
Let be a periodic time scale. The purpose of this paper is to use a modification of Krasnoselskii’s fixed point theorem due to Burton to prove the existence of periodic solutions on time scale of the nonlinear dynamic equation with variable delay , , where is the -derivative on and is the -derivative on . We invert the given equation to obtain an equivalent integral equation from which we define a fixed point mapping written as a sum of a large contraction and a compact map. We show...
Finite Equations in n Unknowns
Fonctions booléennes très incomplètes. Représentation par des sommes de monômes
Formulas of the general solutions of Boolean equations.
Four-part semigroups - semigroups of Boolean operations
Four-part semigroups form a new class of semigroups which became important when sets of Boolean operations which are closed under the binary superposition operation f + g := f(g,...,g), were studied. In this paper we describe the lattice of all subsemigroups of an arbitrary four-part semigroup, determine regular and idempotent elements, regular and idempotent subsemigroups, homomorphic images, Green's relations, and prove a representation theorem for four-part semigroups.