Hadrien Jeanne

Approximate regular expressions and their derivatives

Several studies have been achieved to construct a finite automaton that recognizes the set of words that are at a bounded distance from some word of a given language. In this paper, we introduce a new family of regular operators based on a generalization of the notion of distance and we define a new family of expressions, the approximate regular expressions. We compute Brzozowski derivatives and Antimirov derivatives of such operators, which allows us to provide two recognizers for the language denoted by any approximate regular expression.

AN EFFICIENT ALGORITHM TO TEST WHETHER A BINARY AND PROLONGEABLE REGULAR LANGUAGE IS GEOMETRICAL

Our aim is to present an efficient algorithm that checks whether a binary regular language is geometrical or not, based on specific properties of its minimal deterministic automaton. Geometrical languages have been introduced in the framework of off-line temporal validation of real-time softwares. Actually, validation can be achieved through both a model based on regular languages and a model based on discrete geometry. Geometrical languages are intended to develop a link between these two models. The regular case is of practical interest regarding to implementation features, which motivates the design of an efficient geometricity test addressing the family of regular languages.

Two-Sided Derivatives for Regular Expressions and for Hairpin Expressions

The aim of this paper is to design the polynomial construction of a finite recognizer for hairpin completions of regular languages. This is achieved by considering completions as new expression operators and by applying derivation techniques to the associated extended expressions called hairpin expressions. More precisely, we extend partial derivation of regular expressions to two-sided partial derivation of hairpin expressions and we show how to deduce a recognizer for a hairpin expression from its two-sided derived term automaton, providing an alternative proof of the fact that hairpin completions of regular languages are linear context-free.

Geometricity of binary regular languages

Our 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.

Regular geometrical languages and tiling the plane

We show that if a binary language L is regular, prolongable and geometrical, then it can generate, on certain assumptions, a p1 type tiling of a part of N2. We also show that the sequence of states that appear along a horizontal line in such a tiling only depends on the shape of the tiling sub-figure and is somehow periodic.

Geometrical regular languages and linear diophantine equations

We present a new method for checking whether a regular language over an arbitrarily large alphabet is semi-geometrical or whether it is geometrical. This method makes use first of the partitioning of the state diagram of the minimal automaton of the language into strongly connected components and secondly of the enumeration of the simple cycles in each component. It is based on the construction of systems of linear Diophantine equations the coefficients of which are deduced from the the set of simple cycles. This paper addresses the case of a strongly connected graph.

Decidability of geometricity of regular languages

Geometrical languages generalize languages introduced to model temporal validation of real-time softwares. We prove that it is decidable whether a regular language is geometrical. This result was previously known for binary languages.

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

Given an arbitrarily large alphabet @S, we consider the family of regular languages over @S 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.

Testing Whether a Binary and Prolongeable Regular Language L Is Geometrical or Not on the Minimal Deterministic Automaton of Pref(L)

Our aim is to present an efficient algorithm that checks whether a binary and prolongeable regular language is geometrical or not, based on specific properties of its minimal deterministic automaton. Geometrical languages have been introduced in the framework of off-line temporal validation of real-time softwares. Actually, validation can be achieved through both a model based on regular languages and a model based on discrete geometry. Geometrical languages are intended to develop a link between these two models. The regular case is of practical interest regarding to implementation features, which motivates the design of an efficient geometricity test addressing the family of regular languages.