Le cylindre des langages linéaires

AbstractDefine a cylinder to be a family of languages which is closed under inverse homomorphisms and intersection with regular sets. A number of well-known families of languages are cylinders:—CFL, the family of context-free languages, is a principal cylinder, i.e. the smallest cylinder containing a languageLO described in [6].—the family of deterministic context-free languages is proved to be a nonprincipal cylinder in [7].—the family of unambiguous context-free languages is a cylinder: to prove that it is not principal seems to be a very hard problem. In this paper we prove that Lin, the family of linear context-free languages, is a nonprincipal cylinder. This is achieved in the standard way by exhibiting a sequence of languages Sn, n∈N, such that Lin is the union of all the principal cylinders generated by these languages and is not the union of any finite number of these cylinders.This leaves open the problem raised by Sheila Greibach of whether there exists a languageL such that every linear context-free language is the image ofL in some inverse gsm mapping.