Consider the field F2n . Its elements are presented as polynomials from F2[x] modulo some irreducible polynomial of degree n. This polynomial can be found in time polynomial in n, as well as the matrix that related two representation corresponding to different irreducible polynomials [2]. Therefore, we do not need to specify a choice of the irreducible polynomial speaking about polynomial reduc...

Polynomial threshold gates are basic processing units of an artificial neural network. When the input vectors are binary vectors, these gates correspond to Boolean functions and can be analyzed via their polynomial representations. In practical applications, it is desirable to find a polynomial representation with the smallest number of terms possible, in order to use the least possible number ...

This paper investigates second-order representations in the sense of Kawamura and Cook for spaces of integrable functions that regularly show up in analysis. It builds upon prior work about the space of continuous functions on the unit interval: Kawamura and Cook introduced a representation inducing the right complexity classes and proved that it is the weakest second-order representation such ...

Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation. We show that within this representation the polynomial greatest common divisor and factorization problems, as well as the problem of extracting the numerator and denominator of a rational function, can all b...

We show that every equivariant polynomial automorphism of a-representation and of the reduction of an irreducible-representation is a multiple of the identity.

In this paper, we introduce weighted graph bundles and study their characteristic polynomial. In particular, we show that the characteristic polynomial of a weighted K2 (K2)bundles over a weighted graph F can be expressed as a product of characteristic polynomials two weighted graphs whose underlying graphs are F As an application, we compute the signature of a link whose corresponding weighted...

The goal of this paper is to propose observer-based controllers, either in state-space form or in polynomial representation, for fractional diierential systems. As for linear diierential systems of integer order, polynomial representation will allow us to take advantage of the Youla parametrization in order to asymptotically reject some perturbations. This will be illustrated on a worked-out ex...