The paper presents one concept of decomposition methods dedicated to PAL-based CPLDs. The proposed approach is an alternative to the classical one, which is based on two-level minimization of separate single-output functions. The key idea of the algorithm is to search for free blocks that could be implemented in PAL-based logic blocks containing a limited number of product terms. In order to better exploit the number of product terms, two-stage decomposition and BDD-based decomposition are to be...

Spectral methods constitute a useful tool in the analysis and synthesis of Boolean functions, especially in cases when other methods reduce to brute-force search procedures. There is renewed interest in the application of spectral methods in this area, which extends also to the closely connected concept of the autocorrelation function, for which spectral methods provide fast calculation algorithms. This paper discusses the problem of spectral decomposition of Boolean functions using the Walsh transform...

The depth hierarchy results for monotone circuits of Raz and McKenzie [5] are extended to the case of monotone circuits of semi-unbounded fan-in. It follows that the inclusions $N{C}^i\subseteq SA{C}^i\subseteq A{C}^i$ are proper in the monotone setting, for every $i\ge 1$.

The depth hierarchy results for monotone circuits of Raz and McKenzie [5] are extended to the case of monotone circuits of semi-unbounded fan-in. It follows that the inclusions NCi ⊆ SACi ⊆ ACi are proper in the monotone setting, for every i ≥ 1.

An optimization method of the logic circuit of a Mealy finite-state machine is proposed. It is based on the transformation of object codes. The objects of the Mealy FSM are internal states and sets of microoperations. The main idea is to express the states as some functions of sets of microoperations (internal states) and tags. The application of this method is connected with the use of a special code converter in the logic circuit of an FSM. An example of application is given. The effectiveness...

Nous donnons ici deux résultats sur le déterminant $\zeta$-régularisé ${det}_{\zeta }A$ d’un opérateur de Schrödinger $A={\Delta }_g+V$ sur une variété compacte $ℳ$. Nous construisons, pour $ℳ=S^1\times S^1$, une suite $(G_n,{\rho }_n,{\Delta }_n)$ où $G_n$ est un graphe fini qui se plonge dans $ℳ$ via ${\rho }_n$ de telle manière que ${\rho }_n\left(G_n\right)$ soit une triangulation de $ℳ$ et où ${\Delta }_n$ est un laplacien discret sur $G_n$ tel que pour tout potentiel $V$ sur $ℳ$, la suite de réels $det({\Delta }_n+V)$ converge après renormalisation vers ${det}_{\zeta }({\Delta }_g+V)$. Enfin, nous donnons sur toute variété riemannienne compacte $(ℳ,g)$ de dimension inférieure ou égale à $3$...

This paper develops a new approach to double fault isolation in linear systems with the aid of directional residuals. The method of residual generation for computational as well as internal forms is applied. Isolation of double faults is based on the investigation of the coplanarity of the residual vector with the planes defined by the individual pairs of directional fault vectors. Additionally, the method of designing secondary residuals, which are structured and directional, is proposed. These...

Nous présentons un modèle mathématique permettant de reproduire le spectre expérimental des fréquences dans un composant électronique appelé boucle ouverte. Le spectre semble s’organiser suivant une contrainte de nature diophantienne sur les fréquences. Sa structure peut donc se comprendre via une étude de l’ensemble des fractions continues en fonction de leur longueur et de la taille des quotients partiels.

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...

In this paper, dual synchronization of a hybrid system containing a chaotic Colpitts circuit and a Chua’s circuit, connected by an additive white Gaussian noise (AWGN) channel, is studied via numeric simulations. The extended Kalman filter (EKF) is employed as the response system to achieve the dual synchronization. Two methods are proposed and investigated. The first method treats the combination of a Colpitts circuit and a Chua’s circuit as a higher- dimensional system, while the second method...

It is well known that the k-ary n-cube has been one of the most efficient interconnection networks for distributed-memory parallel systems. A k-ary n-cube is bipartite if and only if k is even. Let (X,Y) be a bipartition of a k-ary 2-cube (even integer k ≥ 4). In this paper, we prove that for any two healthy vertices u ∈ X, v ∈ Y, there exists a hamiltonian path from u to v in the faulty k-ary 2-cube with one faulty vertex in each part.

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...