@article{LATTEUX198314,
    Abstract = {Nous {\'e}tudions les langages {\'a} un compteur, c'est-{\'a}-dire, les langages appartenant {\'a} Rocl, le c{\^o}ne rationnel engendr{\'e} par D'1∗, le langage de semi-Dyck sur une lettre. Nous montrons que tout g{\'e}n{\'e}rateur de Rocl est bifid{\`e}le et qu'il existe un langage {\'a} un compteur qui domine tous les autres par transduction rationnelle pr{\'e}servant les longueurs. Nous {\'e}tablissons, ensuite, que le lemme d'it{\'e}ration des langages lin{\'e}aires est presque vrai pour les langages {\'a} un compteur. Enfin, nous prouvons que Rocl ne contient aucune FAL non rationnelle et que, si Rocl est inclus dans la plus petite FAL contenant un c{\^o}ne rationnel L clos par union, alors Rocl est inclus dans L. De m{\^e}me, si Rocl est inclus dans la plus petite FAL close par substitution contenant un cone rationnel alg{\'e}brique L, alors Rocl est inclus dans L. We study restricted one-counter languages, that is, languages belonging to Rocl, the full trio generated by D'1∗, the restricted Dyck language over one pair of parentheses. We show that every generator of Rocl is a bifaithful one and that there exists a one-counter language which dominates the other ones by length-preserving rational transduction. Then, we establish that the pumping lemma for linear languages is almost true for restricted one-counter languages. Finally, we prove that Rocl contains no nonrational AFL and, if Rocl is included in the smallest full AFL containing a full semi-AFL L, then Rocl is included in L. If Rocl is included in the smallest full AFL closed under substitution containing a context-free full trio L, then Rocl is included in L.},
    Author = {Latteux, Michel},
    File = {Langages á un Compteur - Latteux (0) (0) - a - a - y.pdf},
    ISSN = {0022-0000},
    Journal = {Journal of Computer and System Sciences},
    Number = {1},
    Pages = {14 - 33},
    Title = {Langages {\'a} un Compteur},
    URL = {http://www.sciencedirect.com/science/article/pii/0022000083900181},
    Volume = {26},
    Year = {1983},
    bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/0022000083900181},
    bdsk-url-2 = {http://dx.doi.org/10.1016/0022-0000(83)90018-1},
    date-added = {2016-09-27 12:06:27 +0000},
    date-modified = {2016-09-27 12:06:27 +0000},
    doi = {10.1016/0022-0000(83)90018-1}
}

@article{LATTEUX198314, Abstract = {Nous {\'e}tudions les langages {\'a} un compteur, c'est-{\'a}-dire, les langages appartenant {\'a} Rocl, le c{\^o}ne rationnel engendr{\'e} par D'1∗, le langage de semi-Dyck sur une lettre. Nous montrons que tout g{\'e}n{\'e}rateur de Rocl est bifid{`e}le et qu'il existe un langage {\'a} un compteur qui domine tous les autres par transduction rationnelle pr{\'e}servant les longueurs. Nous {\'e}tablissons, ensuite, que le lemme d'it{\'e}ration des langages lin{\'e}aires est presque vrai pour les langages {\'a} un compteur. Enfin, nous prouvons que Rocl ne contient aucune FAL non rationnelle et que, si Rocl est inclus dans la plus petite FAL contenant un c{\^o}ne rationnel L clos par union, alors Rocl est inclus dans L. De m{\^e}me, si Rocl est inclus dans la plus petite FAL close par substitution contenant un cone rationnel alg{\'e}brique L, alors Rocl est inclus dans L. We study restricted one-counter languages, that is, languages belonging to Rocl, the full trio generated by D'1∗, the restricted Dyck language over one pair of parentheses. We show that every generator of Rocl is a bifaithful one and that there exists a one-counter language which dominates the other ones by length-preserving rational transduction. Then, we establish that the pumping lemma for linear languages is almost true for restricted one-counter languages. Finally, we prove that Rocl contains no nonrational AFL and, if Rocl is included in the smallest full AFL containing a full semi-AFL L, then Rocl is included in L. If Rocl is included in the smallest full AFL closed under substitution containing a context-free full trio L, then Rocl is included in L.}, Author = {Latteux, Michel}, File = {Langages á un Compteur - Latteux (0) (0) - a - a - y.pdf}, ISSN = {0022-0000}, Journal = {Journal of Computer and System Sciences}, Number = {1}, Pages = {14 - 33}, Title = {Langages {\'a} un Compteur}, URL = {http://www.sciencedirect.com/science/article/pii/0022000083900181}, Volume = {26}, Year = {1983}, bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/0022000083900181}, bdsk-url-2 = {http://dx.doi.org/10.1016/0022-0000(83)90018-1}, date-added = {2016-09-27 12:06:27 +0000}, date-modified = {2016-09-27 12:06:27 +0000}, doi = {10.1016/0022-0000(83)90018-1} }