On the Complexity of Computing the Profinite Closure of a Rational Language

International audienceThe profinite topology is used in rational languages classification. In particular, several important decidability problems, related to the Malcev product, reduce to the computation of the closure of a rational language in the profinite topology. It is known that given a rational language by a deterministic automaton, computing a deterministic automaton accepting its profinite closure can be done with an exponential upper bound. This paper is dedicated the study of a lower bound for this problem: we prove that in some cases, if the alphabet contains at least three letters, it requires an exponential time

Seed: an easy to use random generator of recursive data structures for testing

Random testing represents a simple and tractable way for software assessment. This paper presents the \seed tool that can be used for the uniform random generation of recursive data structures such as labelled trees and logical formulas. We show how \seed can be used in several testing contexts, from model based testing to performance testing. Generated data structures are defined by grammar-like rules, given in an XML format, multiplying \seed possible applications. Seed is based on combinatorial techniques, and can generate uniformly at random k structures of size $n$ with a time complexity in O(n^2+ kn\log n). Finally, \seed is available as a free Java application and a great effort has been made to make it easy-to-use

Towards Formalizing QoS of Web Services with Weighted Automata

Web services (WSs) are used more and more as components of distributed applications with a goal to resolve complex tasks that simple services cannot. This use of WSs is connected to the emergence of languages like WS-BPEL which allows describing the external behaviour of WSs on top of the service interfaces. The use of WSs as components of distributed applications implies the possibility to change a failing service for another which can do at least the same things as the replaced service. The composition issues are also of particular interest to WSs users. Different solutions have been proposed during the last years to check such properties, but, to our knowledge, none of them takes QoS aspects into account. This paper introduces underpinnings and a tool for verifying WSs substitutivity and well-formed composition while considering WSs costs such as the execution time of the different operations provided by WSs

Approximation based tree regular model checking

International audienceThis paper addresses the following general problem of tree regular model-checking: decide whether $\R^*(L)\cap L_p =\emptyset$ where $\R^*$ is the reflexive and transitive closure of a successor relation induced by a term rewriting system $\R$, and $L$ and $L_p$ are both regular tree languages. We develop an automatic approximation-based technique to handle this -- undecidable in general -- problem in most practical cases, extending a recent work by Feuillade, Genet and Viet Triem Tong. We also make this approach fully automatic for practical validation of security protocols

Approximations par réécriture pour deux problèmes indécidables

National audiencePour vérifier des propriétés de sûreté ou de (non-)atteignabilité par model-checking régulier, on se concentre sur une modélisation des configurations accessibles du système par des langages réguliers et des relations d'évolution par des systèmes de réécriture. Le problème d'atteignabilité est indécidable dans de nombreux formalismes, et l'approche générale consiste à étudier et/ou à combiner des cas particuliers. Nous nous intéressons à l'approche par approximation pour semi-décider ce problème de vérification. Dans ce papier, nous exploitons l'analyse d'atteignabilité pour deux problèmes indécidables pour les machines de Turing : vacuité d'un langage et appartenance d'un mot à un langage. Nous proposons une modélisation et montrons comment les approximations par réécriture permettent de semi-décider ces problèmes. Cette approche a été implantée et expérimentée

Random Generation of Positive TAGEDs wrt. the Emptiness Problem

Tree automata are a widely used formalism in Computer Science. Since their creation in the fifties, numerous more expressive extensions have been proposed. Unfortunately, the decision problems associated with these extensions are quite often undecidable or in prohibitive classes of algorithmic complexity (NP-complete or worse), and little work has gone into finding efficient heuristics for them. Beyond the inherent difficulty of those problems, a common hitch in this line of research is the experimental evaluation of new algorithms. As those extensions of tree automata have remained in chiefly theoretical spheres, there are no established testbeds from the "real world" against which to quantify the efficiency (or lack thereof) of new algorithms. Failing that, there is a need to generate suitable testbeds at random. Regrettably, there is little material in the literature regarding random generation of tree automata, and none at all regarding extensions such as Tree Automata with Global Equality and Disequality Constraints (TAGEDs). It should also be noted that what little material there is does not concern itself with the interest of the generated automata wrt. specific decision problems. In this report we present a scheme for random generation of positive TAGEDs, with a focus on making them interesting wrt. the Emptiness problem

Controlling and Assessing Correlations of Cost Matrices in Heterogeneous Scheduling

International audienceThis paper considers the problem of allocating independent tasks to unrelated machines such as to minimize the maximum completion time. Testing heuristics for this problem requires the generation of cost matrices that specify the execution time of each task on each machine. Numerous studies showed that the task and machine heterogeneities belong to the properties impacting heuristics performance the most. This study focuses on orthogonal properties, the average correlations between each pair of rows and each pair of columns, which is a proximity measure with uniform instances 1. Cost matrices generated with a novel generation method show the effect of these correlations on the performance of several heuristics from the literature. In particular, EFT performance depends on whether the tasks are more correlated than the machines and HLPT performs the best when both correlations are close to one

List and shelf schedules for independent parallel tasks to minimize the energy consumption with discrete or continuous speeds

International audienceScheduling independent tasks on a parallel platform is a widely-studied problem, in particular when the goal is to minimize the total execution time, or makespan (P||C_max problem in Graham's notations). Also, many applications do not consist of sequential tasks, but rather parallel tasks, either rigid, with a fixed degree of parallelism, or moldable, with a variable degree of parallelism (i.e., for which we can decide at the execution on how many processors they are executed). Furthermore, since the energy consumption of data centers is a growing concern, both from an environmental and economical point of view, minimizing the energy consumption of a schedule is a main challenge to be addressed. One can then decide, for each task, on how many processors it is executed, and at which speed the processors are operated, with the goal to minimize the total energy consumption. We further focus on co-schedules, where tasks are partitioned into shelves, and we prove that the problem of minimizing the energy consumption remains NP-complete when static energy is consumed during the whole duration of the application. We are however able to provide an optimal algorithm for the schedule within one shelf, i.e., for a set of tasks that start at the same time. Several approximation results are derived, both with discrete and continuous speed models, and extensive simulations are performed to show the performance of the proposed algorithms