The Bottom-Up Position Tree Automaton, the Father Automaton and their Compact Versions

The conversion of a given regular tree expression into a tree automaton has been widely studied. However, classical interpretations are based upon a Top-Down interpretation of tree automata. In this paper, we propose new constructions based on the Gluskov's one and on the one of Ilie and Yu one using a Bottom-Up interpretation. One of the main goals of this technique is to consider as a next step the links with deterministic recognizers, consideration that cannot be performed with classical Top-Down approaches. Furthermore, we exhibit a method to factorize transitions of tree automata and show that this technique is particularly interesting for these constructions, by considering natural factorizations due to the structure of regular expression.Comment: extended version of a paper accepted at CIAA 201

A General Framework for the Derivation of Regular Expressions

The aim of this paper is to design a theoretical framework that allows us to perform the computation of regular expression derivatives through a space of generic structures. Thanks to this formalism, the main properties of regular expression derivation, such as the finiteness of the set of derivatives, need only be stated and proved one time, at the top level. Moreover, it is shown how to construct an alternating automaton associated with the derivation of a regular expression in this general framework. Finally, Brzozowski's derivation and Antimirov's derivation turn out to be a particular case of this general scheme and it is shown how to construct a DFA, a NFA and an AFA for both of these derivations.Comment: 22 page

Root-Weighted Tree Automata and their Applications to Tree Kernels

In this paper, we define a new kind of weighted tree automata where the weights are only supported by final states. We show that these automata are sequentializable and we study their closures under classical regular and algebraic operations. We then use these automata to compute the subtree kernel of two finite tree languages in an efficient way. Finally, we present some perspectives involving the root-weighted tree automata

Some Combinatorial Operators in Language Theory

Multitildes are regular operators that were introduced by Caron et al. in order to increase the number of Glushkov automata. In this paper, we study the family of the multitilde operators from an algebraic point of view using the notion of operad. This leads to a combinatorial description of already known results as well as new results on compositions, actions and enumerations.Comment: 21 page

Construction of rational expression from tree automata using a generalization of Arden's Lemma

Arden's Lemma is a classical result in language theory allowing the computation of a rational expression denoting the language recognized by a finite string automaton. In this paper we generalize this important lemma to the rational tree languages. Moreover, we propose also a construction of a rational tree expression which denotes the accepted tree language of a finite tree automaton

State complexity of catenation combined with a boolean operation: a unified approach

In this paper we study the state complexity of catenation combined with symmetric difference. First, an upper bound is computed using some combinatoric tools. Then, this bound is shown to be tight by giving a witness for it. Moreover, we relate this work with the study of state complexity for two other combinations: catenation with union and catenation with intersection. And we extract a unified approach which allows to obtain the state complexity of any combination involving catenation and a binary boolean operation

Bottom Up Quotients and Residuals for Tree Languages

In this paper, we extend the notion of tree language quotients to bottom-up quotients. Instead of computing the residual of a tree language from top to bottom and producing a list of tree languages, we show how to compute a set of k-ary trees, where k is an arbitrary integer. We define the quotient formula for different combinations of tree languages: union, symbol products, compositions, iterated symbol products and iterated composition. These computations lead to the definition of the bottom-up quotient tree automaton, that turns out to be the minimal deterministic tree automaton associated with a regular tree language in the case of the 0-ary trees

Multilinear representations of Free PROs

We describe a structure of PRO on hypermatrices. This structure allows us to define multilinear representations of PROs and in particular of free Pros. As an example of applications, we investigate the relations of the representations of Pros with the theory of automata.Comment: 39 page

Etude d'implémentations MPI dans une grille de calcul

National audienceThis paper presents an evaluation on the GRID'5000 platform of four MPI implementation: MPICH2, MPICH-Madeleine, OpenMPI et GridMPI. The comparison is based on a simple pingpong and the NAS parallel benchmarks. We show that GridMPI has the best results with regards to performances on the Grid if the implementation is well tuned. This paper details which parameters should be tuned.De nos jours, les grappes de PC ou clusters sont souvent interconnectés par des réseaux longue-distance de manière à former une grille afin d'offrir à un grand nombre d'utilisateurs un nombre plus conséquent de ressources. MPI, la bibliothèque de communication la plus utilisée pour les applications parallèles, a été efficacement implémentée dans un contexte de clusters. Deux caractéristiques des grilles, les réseaux longue-distance et l'hétérogénéité des processeurs et des réseaux, posent la question de l'efficacité de MPI sur les grilles. Cet article présente une évaluation sur la grille de recherche française GRID'5000, de 4 implémentations récentes de MPI : MPICH2, MPICH-Madeleine, OpenMPI et GridMPI. La comparaison est basée sur un pingpong, les NAS Parallel Benchmarks. Nous mettons en évidence les différences de performance obtenues avec les 4 implé- mentations. GridMPI montre les meilleures performances. L'exécution d'applications MPI sur la grille peut être bénéfique à condition de régler finement certains paramètres des implémentations. Cet article détaille les para- mètres mis en jeu et leurs réglages

Comparison and tuning of MPI implementations in a grid context

Today, clusters are often interconnected by long distance networks within grids to offer a huge number of available ressources to a range of users. MPI, the standard communication library used to write parallel applications, has been implemented for clusters. Two main features of grids: long distance networks and technological heterogeneity, raise the question of MPI efficiency in grids. This report presents an evaluation of four recent MPI implementations (MPICH2, MPICH-Madeleine, OpenMPI and GridMPI) in the french research grid: Grid'5000. The comparison is based on the execution of pingpong, NAS Parallel Benchmarks and a real application in geophysics. We show that this implementations present performance differences. Executing MPI applications on the grid can be beneficial if the parameters are well tuned. The paper details the tuning required on each implementation to get the best performances