Épaississement d'une hypersurface algébrique réelle

Variétés bipolaires et résolution d’une équation polynomiale réelle

Nous avons décrit précédemment un algorithme efficace qui exhibe un point représentatif (algébrique) par composante connexe d’une intersection complète réelle lisse. Ce processus est basé sur l’exploitation des propriétés géométriques des variétés polaires génériques et sa complexité est intrinsèque au problème. Nous introduisons ici une construction naturelle nous permettant de traiter le cas ...

Un langage algébrique particulier

— 11 is well-known that thefamily of context-free languages is a full principal AFL. It thus contains a largestfûll sub-AFL, denoted Nge, consisting ofthe languages which are notfull generators. One ofthe major problems (still unsolved) is to know whether this AFL is principal or not. The main resuit in this direction states that Ngestrictly contains thefamily Gre ofthe Greibach languages ( — t...

Extending DUNE: The dune-xt modules

We present our effort to extend and complement the core modules of the Distributed and Unified Numerics Environment DUNE (http://dune-project.org) by a well tested and structured collection of utilities and concepts. We describe key elements of our four modules dune-xt-common, dune-xt-grid, dune-xt-la and dune-xt-functions, which aim at further enabling the programming of generic algorithms wit...

Indécidabilité des Corps de Courbe Réelle

Test de conformité : une approche algébrique

In this article, we propose a formalization of conformance testing with respect to algebraic specifications. We interpret functional behavior of programs with the help of algebraic models. We materialize abstract tests extracted from the specification with concrete tests written in a given programming language. This double bridge allows us to link the semantic correctness of a program with the ...