arXiv subjects

Ludovic Mignot

Publications and source records attributed to Ludovic Mignot.

23 records · Page 2Linked to original sources

arXiv2014

An Efficient Algorithm for the Equation Tree Automaton via the $k$-C-Continuations

Champarnaud and Ziadi, and Khorsi et al. show how to compute the equation automaton of word regular expression $E$ via the $k$-C-Continuations. Kuske and Meinecke extend the computation of the equation automaton to a regular tree expression $E$ over a ranked alphabet $Σ$ and produce a $O(R\cdot|E|^2)$ time and space complexity algorithm, where $R$ is the maximal rank of a symbol occurring in $Σ$ and $|E|$ is the size of $E$. In this paper, we give a full description of the algorithm based on the acyclic minimization of Revuz. Our algorithm, which is performed in an $O(|Q|\cdot|E|)$ time and space complexity, where $|Q|$ is the number of states of the produced automaton, is more efficient than the one obtained by Kuske and Meinecke.

cs.FL↗

arXiv2013

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.

cs.FL↗

arXiv2012

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.

cs.FL↗

arXiv2012

Derivatives of Approximate Regular Expressions

Our aim is to construct a finite automaton recognizing the set of words that are at a bounded distance from some word of a given regular language. We define new regular operators, the similarity operators, based on a generalization of the notion of distance and we introduce the family of regular expressions extended to similarity operators, that we call AREs (Approximate Regular Expressions). We set formulae to compute the Brzozowski derivatives and the Antimirov derivatives of an ARE, which allows us to give a solution to the ARE membership problem and to provide the construction of two recognizers for the language denoted by an ARE. As far as we know, the family of approximative regular expressions is introduced for the first time in this paper. Classical approximate regular expression matching algorithms are approximate matching algorithms on regular expressions. Our approach is rather to process an exact matching on approximate regular expressions.

cs.FL↗

arXiv2012

Some Combinatorial Operators in Language Theory

Multitildes are regular operators that were introduced by Caron et al. in order to increase the number of Glushkov automata. In this paper, we study the family of the multitilde operators from an algebraic point of view using the notion of operad. This leads to a combinatorial description of already known results as well as new results on compositions, actions and enumerations.

cs.FL↗