Geometrical Languages

International audienceOur 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