Rodier, François
Published in
Designs, Codes and Cryptography

Boolean functions on the space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_{2}^{m}$$\end{document} are not only important in the theory of error-correcti...

Balasubramanian, P Edwards, D A

Structuring and mapping of a Boolean function is an important problem in the design of digital combinatorial circuits. Library aware constructive decomposition offers a solution to this problem. Compact multi-level representation of binary networks, based on simple circuit structures, such as AND-Inverter Graphs (AIG) [1] [5], NAND graphs, OR-Inver...

Kleine Büning, Hans Subramani, K. Zhao, Xishun
Published in
Journal of Automated Reasoning

In this paper, we introduce the notion of models for quantified Boolean formulas. For various classes of quantified Boolean formulas and various classes of Boolean functions, we investigate the problem of determining whether a model exists. Furthermore, we show for these classes the complexity of the model checking problem, which is to check whethe...

Férard, Eric Rodier, François

We study the nonlinearity of functions defined on a finite field with 2^m elements which are the trace of a polynomial of degree 7 or more general polynomials of binary degree equal to 3. We show that for m odd such functions have rather good nonlinearity properties. We use for that recent results of Maisner and Nart about zeta functions of supersi...

Rodier, François Férard, Eric

Jarrah, Abdul Salam Raposa, Blessilda Laubenbacher, Reinhard
Published in
Physica D. Nonlinear phenomena

This paper focuses on the study of certain classes of Boolean functions that have appeared in several different contexts. Nested canalyzing functions have been studied recently in the context of Boolean network models of gene regulatory networks. In the same context, polynomial functions over finite fields have been used to develop network inferenc...

Couceiro, Miguel Lehtonen, Erkko

Let A be a finite set and B an arbitrary set with at least two elements. The arity gap of a function f:Aⁿ→B is the minimum decrease in the number of essential variables when essential variables of f are identified. A non-trivial fact is that the arity gap of such B-valued functions on A is at most |A|. Even less trivial to verify is the fact that t...

Bibilo, P. N.
Published in
Automatic Control and Computer Sciences

It is proposed that the apparatus of logic equations be used to achieve an exact solution of the problem of joint decomposition of a system of Boolean functions with respect to a two-block partitioning of the set of arguments.

Sharankhaev, I. K.
Published in
Siberian Mathematical Journal

Under study are the representations of Boolean functions by formulas. We offer a criterion for the Boolean functions to be repetition-free in the base {V,·, −0, 1, x1(x2 V x3x4) V x5(x3 V x2x4)}.

Lehtonen, Erkko Szendrei, Ágnes

For each clone C on a set A there is an associated equivalence relation, called C-equivalence, on the set of all operations on A, which relates two operations iff each one is a substitution instance of the other using operations from C. In this paper we prove that if C is a discriminator clone on a finite set, then there are only finitely many C-eq...