Related papers: Practical Groebner Basis Computation
It has been shown in recent years that quantum information has a topological nature (\cite{AC}, \cite{Co}, \cite{Co2}). In \cite{V}, Vicary undergoes the study of quantum algorithms using this new topological approach. The advantage of this…
As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available…
We simulate Grover's algorithm in a classical computer by means of a stochastic method using the Hubbard-Stratonovich decomposition of n-qubit gates into one-qubit gates integrated over auxiliary fields. The problem reduces to finding the…
Applied research in graph algorithms and combinatorial structures needs comprehensive and versatile software libraries. However, the design and the implementation of flexible libraries are challenging activities. Among the other problems…
The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are…
We present here a new approach for computing Gr\"obner bases for bilateral modules over an effective ring. Our method is based on Weispfenning notion of restricted Gr\"obner bases and related multiplication.
Gibbs sampling is fundamental to a wide range of computer algorithms. Such algorithms are set to be replaced by physics based processors$-$be it quantum or stochastic annealing devices$-$which embed problem instances and evolve a physical…
What can be (machine) learned about the complexity of Buchberger's algorithm? Given a system of polynomials, Buchberger's algorithm computes a Gr\"obner basis of the ideal these polynomials generate using an iterative procedure based on…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
Generalized quasi-cyclic (GQC) codes form a wide and useful class of linear codes that includes thoroughly quasi-cyclic codes, finite geometry (FG) low density parity check (LDPC) codes, and Hermitian codes. Although it is known that the…
This work aims to assess the state of the art of data parallel deep neural network training, trying to identify potential research tracks to be exploited for performance improvement. Beside, it presents a design for a practical C++ library…
Quantum computers and quantum algorithms have made great strides in the last few years and promise improvements over classical computing for specific tasks. Although the current hardware is not yet ready to make real impacts at the time of…
In this paper we introduce a binomial ideal derived from a binary linear code. We present some applications of a Gr\"obner basis of this ideal with respect to a total degree ordering. In the first application we give a decoding method for…
In this talk I give an elementary introduction to the key algorithm used in recent applications of computational algebraic geometry to the subject of string phenomenology. I begin with a simple description of the algorithm itself and then…
It is becoming increasingly clear that, if a useful device for quantum computation will ever be built, it will be embodied by a classical computing machine with control over a truly quantum subsystem, this apparatus performing a mixture of…
The paper introduces a novel representation for Generalized Planning (GP) problems, and their solutions, as C++ programs. Our C++ representation allows to formally proving the termination of generalized plans, and to specifying their…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
We propose and evaluate a novel algorithm for computation of the Duquenne-Guigues basis which combines Close-by-One and LinClosure algorithms. This combination enables us to reuse attribute counters used in LinClosure and speed up the…
This paper is a gentle but rigorous introduction to quantum computing intended for discrete mathematicians. Starting from a small set of assumptions on the behavior of quantum computing devices, we analyze their main characteristics,…
The theory of Groebner Bases originated in the work of Buchberger and is now considered to be one of the most important and useful areas of symbolic computation. A great deal of effort has been put into improving Buchberger's algorithm for…