FREE MONOID THEORY: MAXIMALITY AND COMPLETENESS IN ARBITRARY SUBMONOIDS
Jean Néraud, Carla Selmi · International Journal of Algebra and Computation · 2003
In this paper, we discuss the different notions of local topological density for subsets of the free monoid A*. We introduce the notion of weak completeness for a set X, relatively to an arbitrary submonoid M of A*. For the so-called strongly M-thin codes, we establish that weak completeness is equivalent to maximality in M. This constitutes a new generalization of a famous result due to Schützenberger.