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

L’Échelle de provisions sociales : une validation québécoise

Cet article présente les résultats de la validation québécoise du Social Provisions Scale (Cutrona et Russel, 1989). L'Échelle de provisions sociales a été administrée à 790 personnes au cours de deux études. La première comporte 387 étudiants universitaires de premier cycle et la seconde, 266 personnes de la population générale, 79 bénéficiaires d'aide sociale et 58 personnes ayant reçu un diagnostic relatif à la psychose. Les résultats montrent que l'échelle présente une bonne cohérence interne et une stabilité temporelie satisfaisante, assurant ainsi la fidélité de l'instrument. Les analyses factorielles n'ont pas reproduit exactement le même profil que l'instrument original, toutefois les corrélations modérées entre les différentes provisions sociales soutiennent la validité du construit multidimensionnel du support social. De plus, des analyses de la variance et l'analyse discriminante permettent de constater que les sous-échelles ont un pouvoir discriminant élevé, elles permettent de distinguer la population générale, les bénéficiaires d'aide sociale et les personnes psychotiques. Enfin, les normes sont présentées pour la population générale.This article presents the results of the Quebec validation of the Social Provisions Scale (Cutrona et Russell, 1989). L'échelle de provision sociales was administered to 790 people in the course of two studies. The fist one included 387 university students of first level and the second was realized with 266 people from the general population, 79 welfare recipients and 58 persons with a diagnosis related to psychosis. The results show that the scale presents a good internal coherence and a satisfying temporal stability, thus assuring the fidelity of the instrument. The factorial analyses have not reproduced exactly the same profile as the original instrument, however the moderate correlations between the different social provisions sustain the validity of the multidimensional construct of social support. Moreover, analyses of the variance and the discriminating analysis allow to acknowledge that the sub-scales have a high discriminating power; they allow to distinguish the general population from welfare recipients and people suffering from psychosis. Finally, norms are presented for the general population

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

L’héritage républicain du fédéralisme : Une théorie de l’identité nationale dans les fédérations multinationales

L’évaluation du fédéralisme à la lumière des aspects qui ont mené à la création de la fédération américaine permet de situer ce système politique dans la tradition républicaine de la liberté. Par une historiographie des idées qui ont précédé la révolution américaine et l’établissement du pacte fédéral de 1789, ce texte vise à démontrer en quoi l’idée moderne du fédéralisme est d’abord et avant tout un système politique dont l’objectif consiste à empêcher la domination. À partir de cette historiographie, le présent article vise à établir un cadre normatif pour les politiques identitaires des fédérations multinationales.The evaluation of federalism in light of the elements that led to the creation of the American federation allows us to situate this political system within the republican tradition of liberty. Through a historiography of the ideas that preceded the American Revolution and the federal pact of 1789, this text seeks to demonstrate that the modern idea of federalism is first and foremost that of a political system whose objective is to prevent domination. Based on that historiography, this article aims to establish a normative framework for the politics of identity of multinational federations

Between Renewal and Reevaluation. Milestones in French Historiography on the Restoration

La historiografía francesa sobre la Restauración está marcada por algunos importantes jalones. Poco a poco ha ido escapando de la escritura militante para convertirse en un objeto histórico sometido a una mirada crítica. Aunque durante mucho tiempo fue un período casi abandonado, progresivamente ha ido suscitando mayor interés, algo que puede apreciarse en la ampliación de las temáticas y en el peso creciente de la historia cultural que se infiltra en la historia política, social o religiosa. A pesar de ello, la historia económica o la historia comparada de las Restauraciones en Europa se encuentran todavía en un estado embrionario, a pesar de algunas iniciativas recientemente puestas en marcha.French historiography of the Restoration is marked by some important milestones. It has gradually abandoned militant writing to become a historic object submitted to a critical view. Despite having been for a long time considered as a nearly forgotten period, it has of late aroused a renewed interest which is made evident by the extension of themes, and by the increasing weight of cultural history which penetrates political, social and religious history. However, the economic history, as well as the compared history of the Restorations in Europe still remains embryonic, in spite of some recent initiatives