Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes. In this work, a discrete structure representation of SN P systems with extended rules and without delay is proposed. Specifically, matrices are used to represent SN P systems. In order to represent the computations of SN P systems...

While Generalized Feistel Networks have been widely studied in the literature as a building block of a block cipher, we propose in this paper a unified vision to easily represent them through a matrix representation. We then propose a new class of such schemes called Extended Generalized Feistel Networks well suited for cryptographic applications. We instantiate those proposals into two particu...

In this paper we continue the investigation of simple matrix languages introduced by Ibarra (1970) as a subfamily of matrix languages. Simple matrix languages have many properties similar to those of context-free languages. In the following, we prove that every simple matrix language can be written as a homomorphic image of the intersection of the Dyck context-free language and an equal matrix ...

This article concerns the question: which subsets of R can be represented with Linear Matrix Inequalities, LMIs? This gives some perspective on the scope and limitations of one of the most powerful techniques commonly used in control theory. Also before having much hope of representing engineering problems as LMIs by automatic methods one needs a good idea of which problems can and cannot be re...

An analog circuit synthesis method based on evolutionary circuit techniques is proposed where the chromosome in the genetic algorithm is coded through the use of adjacency matrices. The method assumes that the circuit is described at the behavioral level in order to reduce the simulation time. It is shown that adjacency matrices coding of the chromosome reduces considerably the number of anomal...

By embedding a Toeplitz matrix-vector product (MVP) of dimension n into a circulant MVP of dimension N = 2n+δ−1, where δ can be any nonnegative integer, we present a GF (2) multiplication algorithm. This algorithm leads to a new redundant representation, and it has two merits: 1. The flexible choices of δ make it possible to select a proper N such that the multiplication operation in ring GF (2...

In this paper an integral representation for the Hermite matrix polynomials is given. By means of the exact computation of certain matrix integrals and the integral representation of Hermite matrix polynomials, a formula for the generating function of the product of Her-mite matrix polynomials is obtained. Both the integral representation of the Hermite matrix polynomials and the formula for th...

For generic lower triangular matrices, A, we prove that A ij = P d q=1 H iq G jq for i > j is equivalent to A = M ?1 N where M and N are d+1 banded matrices. A lower triangular matrix A is input balanced of order/rank d if there exists a rank-d matrix B such that AA = I ? BB. We prove that if A is triangular input balanced then generically, A = M ?1 N where M and N are d + 1 banded matrices. Th...

The symmetry of the Hamiltonian describing the asymmetric twin model was partially studied in earlier works, and our aim here is to generalize these results for the open transfer matrix. In this spirit we first prove, that the so called boundary quantum algebra provides a symmetry for any generic – independent of the choice of model – open transfer matrix with a trivial left boundary. In additi...

The aim of this paper is to define and study of the Gegenbauer matrix polynomials of two variables. An explicit representation, a three-term matrix recurrence relations, differential recurrence relations and hypergeometric matrix representation for the Gegenbauer matrix polynomials of two variables are given. The Gegenbauer matrix polynomials are solutions of the matrix differential equations a...