Geometrical Languages

Baptiste Blanpain (1) , Jean-Marc Champarnaud (1) , Jean-Philippe Dubernard (1)

1 LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes

Our aim is to introduce and generalize a class of languages used in off-line temporal validation of real-time softwares. Computing the feasibility of an application consists in checking whether there exists a sequence of execution which allows each task to run without any time error. This can be done with a model based on automata and languages. Because of certain properties of these languages, a model based on discrete geometry can also be used to make the computing time smaller. In this paper, we develop the link between languages and geometry, by defining a new class of languages, which we call geometrical languages. The main result is an algorithm that checks wether a given regular language is geometrical or not, by means of equations with positive integer variables.

Mots clés: Finite automata; languages; discrete geometry; real-time applications; temporal validation

Domaines: Algorithme et structure de données [cs.DS]; Informatique et langage [cs.CL]

Baptiste Blanpain, Jean-Marc Champarnaud, Jean-Philippe Dubernard. Geometrical Languages. LATA'07 (Languages and Automata Theoretical Aspects), Mar 2007, Tarragona, Spain. pp.127—138. ⟨hal-00452953⟩