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

An optimal parallel algorithm to convert a regular expression into its Glushkov automaton

AbstractThe aim of this paper is to describe a CREW-PRAM optimal algorithm which converts a regular expression of size s into its Glushkov automaton in O(log s) time using O(s2log s) processors. This algorithm makes use of the star-normal form of an expression as defined by Brüggemann-Klein (1993) and is based on the sequential algorithm due to Ziadi et al. (1997) which computes an original representation of Glushkov automaton in O(s) time

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

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

Minimisation d'automates non-déterministes, recherche d'expressions dans un texte et comparaison de génomes

Cette thèse débute par la minimisation des automates non-déterministes. Je fournis la preuve d'une technique présentée sans démonstration par Sengoku ainsi que différentes heuristiques, basées sur le calcul de simulations d'états, combinant langages gauches et droits. Ce travail débouche sur une technique de réduction des automates de Büchi. Parallèlement, je m'intéresse à la maîtrise de la complexité en espace de la déterminisation en optimisant la déterminisation partielle. Les thèmes suivants sont plus applicatifs. Le premier concerne la recherche approchée d'expressions secondaires dans le génome au moyen de grammaires algébriques. Je présente une adaptation de l'algorithme de Valiant, puis un algorithme de type CYK pour la recherche approchée d'une hélice simple. Je termine par la recherche d'équipes de gènes communes entre différents génomes, dont un problème sous-jacent est la recherche de composantes connexes communes à plusieurs graphes. J'y présente notre nouvel algorithme traitant le cas de graphes d'intervalles.The initial topic of this thesis is automata minimization. I prove a technique for full minimization that was given unproved by Sengoku, together with heuristics based on state simulations, that combine left and right languages. This work provides a reduction technique for B\"uchi automata. On the other hand, I focus on managing the space complexity of determinisation by an optimized partial determinization.The following is more involved in practical applications. First, I focus on secondary expression search in genome, based on context-free grammars. I give an adaptation of Valiant's algorithm, and a CYK algorithm for single hairpin approximate search. Finally, I investigate gene-team search between several genomes. An underlying problem is the common connected set search between several graphs. I describe our new algorithm that is specific to interval graphs.ROUEN-BU Sciences Madrillet (765752101) / SudocROUEN-BU Sciences (764512102) / SudocSudocFranceF

AUTOMATE, a computing package for automata and finite semigroups

AUTOMATE is a package for symbolic computation on finite automata, extended rational expressions and finite semigroups. On the one hand, it enables one to compute the deterministic minimal automaton of the language represented by a rational expression or given by its table. On the other hand, given the transition table of a deterministic automaton, AUTOMATE computes the associated transition monoid. The regular D-classes structure, and many properties of the elements in the monoid are provided. The program AUTOMATE has been written in C and is quite portable. The user interface includes specialized editors for easy displaying of the computed results

Conception de modèles génériques pour les machines à états finis

Les travaux de ce mémoire s'inscrivent dans le cadre de la théorie des automates et s'articulent autour de la création d'un compilateur de machines à états finis, WFSC, permettant la création et la manipulation d'automates pondérés multibandes à classes de symboles avec identité et non-identité. Ce modèle de machine à états finis est obtenu par généralisation de l'étiquetage des transitions des automates à états finis. La première partie est consacrée à cette généralisation de l'étiquetage. Le but est d'augmenter le pouvoir d'expression et l'efficacité de leur représentation. Nous introduisons la notion de classe de symboles, puis donnons des définitions d'automates, transducteurs, automates multibandes étiquetés par classe de symboles et la notion de relation équi-contrainte comme extension des relations d'identité et de non-identité. La seconde partie est une contribution à l'algorithmique des machines à états finis. Nous étudions d'abord un certain nombre d'opérations pour les machines multibandes pondérées, comme la jointure et l'auto-intersection. Comme il existe une relation avec le problème de la correspondance de Post, nous décrivons une classe de relations rationnelles n-aires pour laquelle l'auto-intersection peut être calculée et donnons les algorithmes correspondants. Ensuite, nous présentons l'étude de la construction de l'automate des follows d'une expression rationnelle à l'aide de la structure ZPC. Une implémentation permettant de comparer cette construction par rapport à la construction classique, a été réalisée. Dans la dernière partie, nous décrivons l'implémentation des machines à états finis virtuelles dans XFST, qui applique le principe de l'évaluation paresseuse aux automates, puis la modélisation des automates pondérés multibandes à classes de symboles avec identité et non-identité dans WFSC. Une technique de programmation améliorant le comportement des classes polymorphes en C++, la bitwise virtuality, est décrite. Enfin, nous terminons par la description de quelques applications afin de démontrer la souplesse d'utilisation à la fois du compilateur et de la bibliothèque WFSC.The work presented in this thesis takes place in the scope of automata theory and connects with the creation of a finite state compiler, WFSC that allows the creation and the processing of symbol class multitape weighted automata with identity and non-identity. This model of finite state machine is obtained by extending the transition labeling of finite state automata. The first part is dedicated to that generalization. The aim is to increase the expressiveness, as well as the compactness of these machines. We introduce the notion of symbol classes and we give definitions for automata, transducers and multitape automata labeled with symbol classes. We introduce in addition the notion for equi-constrained relation that extend the identity and non-identity relations. The second part is a contribution to the algorithmic of finite state machines. At first time, we study a set of operations for weighted multitape automata like join, and the auto-intersection. Due to link with the Post correspondance problem, we describea class of n-ary rational relations for which the auto-intersection can be computed and we give the related algorithms. In second time, we present the construction of the follow automata of a rational expression through the ZPC structure. An implementation was made that allowed the comparison of our construction with respect to the classical one, showing its efficiency in practice. Finally, we describe the implementation of virtual finite state machine inside XFST, that apply the principle of lazy evaluation to finite state machine, and we describe how symbol class multitape weighted automata with identity are modeled in WFSC. A programming technique that improve the behavior of polymorphic classes in C+++, called bitwise virtuality, is described. We finish by describing some applications in order to demonstrate that both the compiler and the WFSC library are easy to use.ROUEN-BU Sciences (764512102) / SudocROUEN-BU Sciences Madrillet (765752101) / SudocTOURS-Polytech'Informat.Product. (372612209) / SudocSudocFranceF