Decidable and undecidable problems about quantum automata

We study the following decision problem: is the language recognized by a quantum finite automaton empty or non-empty? We prove that this problem is decidable or undecidable depending on whether recognition is defined by strict or non-strict thresholds. This result is in contrast with the corresponding situation for probabilistic finite automata for which it is known that strict and non-strict thresholds both lead to undecidable problems.Comment: 10 page

Cosmological Simulations using Grid Middleware

One way to access the aggregated power of a collection of heterogeneous machines is to use a grid middleware, such as DIET, GridSolve or NINF. It addresses the problem of monitoring the resources, of handling the submissions of jobs and as an example the inherent transfer of input and output data, in place of the user. In this paper we present how to run cosmological simulations using the RAMSES application along with the DIET middleware. We will describe how to write the corresponding DIET client and server. The remainder of the paper is organized as follows: Section 2 presents the DIET middleware. Section 3 describes the RAMSES cosmological software and simulations, and how to interface it with DIET. We show how to write a client and a server in Section 4. Finally, Section 5 presents the experiments realized on Grid'5000, the French Research Grid, and we conclude in Section 6.Comment: submitted Nov 200

Revisiting Matrix Product on Master-Worker Platforms

This paper is aimed at designing efficient parallel matrix-product algorithms for heterogeneous master-worker platforms. While matrix-product is well-understood for homogeneous 2D-arrays of processors (e.g., Cannon algorithm and ScaLAPACK outer product algorithm), there are three key hypotheses that render our work original and innovative: - Centralized data. We assume that all matrix files originate from, and must be returned to, the master. - Heterogeneous star-shaped platforms. We target fully heterogeneous platforms, where computational resources have different computing powers. - Limited memory. Because we investigate the parallelization of large problems, we cannot assume that full matrix panels can be stored in the worker memories and re-used for subsequent updates (as in ScaLAPACK). We have devised efficient algorithms for resource selection (deciding which workers to enroll) and communication ordering (both for input and result messages), and we report a set of numerical experiments on various platforms at Ecole Normale Superieure de Lyon and the University of Tennessee. However, we point out that in this first version of the report, experiments are limited to homogeneous platforms

Bandwidth-Centric Allocation of Independent Tasks on Heterogeneous Platforms

In this paper, we consider the problem of allocating a large number of independent, equal-sized tasks to a heterogenerous "grid" computing platform. Such problems arise in collaborative computing efforts like SETI@home. We use a tree to model a grid, where resources can have different speeds of computation and communication, as well as different overlap capabilities. We define a base model, and show how to determine the maximum steady-state throughput of a node in the base model, assuming we already know the throughput of the subtrees rooted at the node's children. Thus, a bottom-up traversal of the tree determines the rate at which tasks can be processed in the full tree. The best allocation is {\em bandwidth-centric}: if enough bandwidth is available, then all nodes are kept busy; if bandwidth is limited, then tasks should be allocated only to the children which have sufficiently small communication times, regardless of their computation power. We then show how nodes with other capabilities -- ones that allow more or less overlapping of computation and communication than the base model -- can be transformed to equivalent nodes in the base model. We also show how to handle a more general communication model. Finally, we present simulation results of several demand-driven task allocatio- n policies that show that our bandwidth-centric method obtains better results than allocating tasks to all processors on a first-come, first serve basis

Use of A Network Enabled Server System for a Sparse Linear Algebra Grid Application

Solving systems of linear equations is one of the key operations in linear algebra. Many different algorithms are available in that purpose. These algorithms require a very accurate tuning to minimise runtime and memory consumption. The TLSE project provides, on one hand, a scenario-driven expert site to help users choose the right algorithm according to their problem and tune accurately this algorithm, and, on the other hand, a test-bed for experts in order to compare algorithms and define scenarios for the expert site. Both features require to run the available solvers a large number of times with many different values for the control parameters (and maybe with many different architectures). Currently, only the grid can provide enough computing power for this kind of application. The DIET middleware is the GRID backbone for TLSE. It manages the solver services and their scheduling in a scalable way.La résolution de systèmes linéaires creux est une opération clé en algèbre linéaire. Beaucoup d’algorithmes sont utilisés pour cela, qui dépendent de nombreux paramètres, afin d’offrir une robustesse, une performance et une consommation mémoire optimales. Le projet GRID-TLSE fournit d’une part, un site d’expertise basé sur l’utilisation de scénarios pour aider les utilisateurs à choisir l’algorithme qui convient le mieux à leur problème ainsi que les paramètres associés; et d’autre part, un environnement pour les experts du domaine leur permettant de comparer efficacement des algorithmes et de définir dynamiquement de nouveaux scénarios d’utilisation. Ces fonctionnalités nécessitent de pouvoir exécuter les logiciels de résolution disponibles un grand nombre de fois,avec beaucoup de valeurs différentes des paramètres de contrôle (et éventuellement sur plusieurs architectures de machines). Actuellement, seule la grille peut fournir la puissance de calcul pour ce type d’applications. L’intergiciel DIETest utilisé pour gérer la grille, les différents services, et leur ordonnancement efficace

Finding a Vector Orthogonal to Roughly Half a Collection of Vectors

International audienceDimitri Grigoriev has shown that for any family of $N$ vectors in the $d$-dimensional linear space E=(\ff{2})^d, there exists a vector in $E$ which is orthogonal to at least $N/3$ and at most $2N/3$ vectors of the family. We show that the range $[N/3,2N/3]$ can be replaced by the much smaller range $[N/2-\sqrt{N}/2,N/2+\sqrt{N}/2]$ and we give an efficient, deterministic parallel algorithm which finds a vector achieving this bound. The optimality of the bound is also investigated

Quantifier rank for parity of embedded finite models

(eng) We prove some lower bounds for quantifier rank of formulas expressing parity of a finite set I of bounded cardinal embedded in an algebraically closed field or an ordered Q-vector space. We show that these bounds are tight when elements of I are known to be linearly independent. In the second part, we prove that strongly minimal structures with quantifier elimination and zero characteristic differentially closed fields admit the active-natural collapse

Ordonnancement et gestion dynamique d'applications sur les grilles de calcul

LYON-ENS Sciences (693872304) / SudocSudocFranceF

Listing all the minimal separators of a planar graph.

(eng) I present an efficient algorithm which lists the minimal separators of a planar graph in O(n) per separator

Synchronization of a line of finite automata with nonuniform delays

(eng) We study the Firing Squad Synchronization Problem with non uniform delays in the case of a line of cells. The problem was solved in the general case by T.~Jiang in time Delta^3. In the case of the line, we improve his result, obtaining the Delta^2. We observe that there does not exist an optimal solution. We also note that the strategy, used here, is the general strategy (Waksman's one) and thus, even in this case, we can break the line in its middle