Validation of distributed periodic real-time systems using CAN protocol with finite automata

International audience‘In a previous work, we have defined a temporal model based on regular languages to validate periodic real-time systems: the feasability decisional process is expressed by means of algebraic operations on languages, such as intersection, Hadamard product, and language center computing. Here, we describe how this model can be used to validate periodic distributed real-time systems. We base this description on the example of the CAN network protocol

Geometrical regular languages and linear Diophantine equations: The strongly connected case

AbstractGiven an arbitrarily large alphabet Σ, we consider the family of regular languages over Σ for which the deterministic minimal automaton has a strongly connected state diagram. We present a new method for checking whether such a language is semi-geometrical or not and whether it is geometrical or not. This method makes use of the enumeration of the simple cycles of the state diagram. It is based on the construction of systems of linear Diophantine equations, where the coefficients are deduced from the set of simple cycles

Scheduling Hard Sporadic Tasks with Regular Languages and Generating Functions

AbstractIn this paper, we consider offline validation of hard real-time systems composed of both periodic and sporadic tasks, embedded on centralized multi-processor architectures. To model hard real-time systems, we use untimed finite automata: each accepted word is a valid operational behavior of the periodic component of the system. Then, by associating generating functions with edges of the automaton, we give a modular decisional technique to decide the feasibility of sporadic tasks

Dirichlet convolution and enumeration of pyramidpolycubes

International audienc

Dirichlet convolution and enumeration of pyramidpolycubes

International audienc

Langages géométriques et polycubes

Ce mémoire comporte deux parties. La première concerne l'étude des langages géométriques au moyen d'outils de la théorie des automates et de géométrie discrète. Un langage géométrique est composé de mots définis sur un alphabet de taille d, en utilisant les images de Parikh de l'ensemble des préfixes de ces mots. Ce qui définit une figure de dimension d. Dans la seconde partie, il est question de l'étude de polycubes de dimension 3. Il y est défini des extensions de certaines própriétés des polyominos en dimension 3. Cela permet de définir différentes classes de polycubes, les polycubes plateaux, s-dirigés et verticalement convexes s-dirigés. Une méthode d'énumération de polycubes dirigés, basée sur la décomposition par strates des polyominos de Temperley, est appliquée à ces classes de polycubes afin de donner leurs fonctions génératrices.This thesis falls into two parts. The first one is about the study of geometrical languages using formal languages and automata theory, as well as discrete geometry tools. A geometrical language is composed of words over an alphabet of size d, using the Parikh images of the set of prefixes of the words. Those images define a figure of dimension d. The second part refers to the study of 3-dimensional polycubes. We define 3-dimensional extensions of some properties of polyominoes. That allow us to define subclasses of polycubes : plateau polycubes, s-directed polycubes and vertically-convex s-directed polycubes. We define an enumeration method over directed polycubes, based on the strate decomposition of polyominoes defined by Temperley, and we use it in order to give the generating functions of the classes of polycubes defined above.ROUEN-BU Sciences Madrillet (765752101) / SudocSudocFranceF

Geometrical Languages

International audienceOur aim is to introduce and generalize a class of languages used in off-line temporal validation of real-time softwares. Computing the feasibility of an application consists in checking whether there exists a sequence of execution which allows each task to run without any time error. This can be done with a model based on automata and languages. Because of certain properties of these languages, a model based on discrete geometry can also be used to make the computing time smaller. In this paper, we develop the link between languages and geometry, by defining a new class of languages, which we call geometrical languages. The main result is an algorithm that checks wether a given regular language is geometrical or not, by means of equations with positive integer variables

Geometricity of Binary Regular Languages

International audienceOur aim is to present an efficient algorithm for checking whether a regular language is geometrical or not, based on specific properties of its minimal automaton. Geometrical languages have interesting theoretical properties and they provide an original model for off-line temporal validation of real-time softwares. As far as implementation is concerned, the regular case is of practical interest, which motivates the design of an efficient geometricity test addressing the family of regular languages. This study generalizes the algorithm designed by the authors for the case of prolongable binary regular languages