Ahmed, Taghreed Younes, Ahmed Elsayed, Ashraf
Published in
Quantum Information Processing

This paper introduces a novel algorithm to synthesize a low-cost reversible circuits for any Boolean function with n inputs represented as a Positive Polarity Reed–Muller expansion. The proposed algorithm applies a predefined rules to reorder the terms in the function to minimize the multi-calculation of common parts of the Boolean function to decr...

Kryvyi, S. L. Opanasenko, V. M.
Published in
Cybernetics and Systems Analysis

This article considers problems of partition of a set of vectors with nonnegative integer coordinates into two classes with respect to a threshold value and a threshold relation using adaptable logical networks. The correctness of the corresponding algorithms for implementing such a partition is proved for an arbitrary threshold value and a dimensi...

Couceiro, Miguel Lehtonen, Erkko
Published in
Order

We investigate the minor order of functions, focusing on upper covers and common upper bounds of pairs of functions. We show that two functions of arities m and n have a common upper bound if and only if they have a common lower bound, and if a common upper bound exists, then there is one of arity m + n − 1. Moreover, we determine the possible esse...

Gajland, Phillip

The growing interest in the Internet of Things (IoT) has led to predictions claiming that by 2020 we can expect to be surrounded by 50 billion Internet connected devices. With more entry points to a network, adversaries can potentially use IoT devices as a stepping stone for attacking other devices connected to the network or the network itself. In...

Suprun, V. P.
Published in
Automatic Control and Computer Sciences

This paper considers the problem of transforametion of Boolean functions into canonical polarized polynomials (Reed–Muller polynomials). Two Shannon functions are introduced to estimate the complexity of Boolean functions in the polynomials class under consideration. We propose three Boolean functions of n variables whose complexity (in terms of th...

Red’kin, N. P.
Published in
Mathematical Notes

Opanasenko, V. N. Kryvyi, S. L.
Published in
Cybernetics and Systems Analysis

This article considers the synthesis of a neural-like Hamming network with a view to implementing the problem of classification of an input set of binary vectors. The formation of a sequence sorted by the Hamming distance as the proximity measure is based on the conversion of cyclic Hamming codes. The correctness of the synthesis of such an impleme...

Dubois, Michel

La cryptologie est une des disciplines des mathématiques, elle est composée de deux sous-ensembles: la cryptographie et la cryptanalyse. Tandis que la cryptographie s'intéresse aux algorithmes permettant de modifier une information afin de la rendre inintelligible sans la connaissance d'un secret, la seconde s'intéresse aux méthodes mathématiques p...

Voronenko, A. A.
Published in
Moscow University Computational Mathematics and Cybernetics

The following problem is considered: Find Boolean function f of n variables with the property that, given any polynomial p of degree at most s, there exists a set of n-tuples such that p is the only polynomial of degree at most s taking the same values as f at these n-tuples. It is shown that for any fixed s and sufficiently large n, such a functio...

Couceiro, Miguel Mercuriali, Pierre Péchoux, Romain

In this paper we compare various normal form representations of Boolean functions. We extend the study of [4], pertaining to the comparison of the asymptotic efficiency of representations that are produced by normal form systems (NFSs) that are factorizations of the clone Ω of all Boolean functions. We identify some properties, such as associativit...