Testing whether a binary and prolongeable regular language L is geometrical or not on the minimal deterministic automaton of Pref(L)

Abstract

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. © 2008 Springer-Verlag Berlin Heidelberg.