Résumé : We investigate the connection between properties of formal languages and properties of their generating series, with a focus on the class of holonomic power series. It is a classical result that regular languages have rational generating series and that the generating series of unambiguous context-free languages are algebraic. This connection between automata theory and analytic combinatorics has been successfully exploited. For instance, Flajolet used it in the eighties to prove the inherent ambiguity of some context-free languages using criteria from complex analysis. Settling a conjecture of Castiglione and Massazza, we establish an interesting link between unambiguous Parikh automata and holonomic power series, which also yields characterizations of inherent ambiguity and algorithmic byproducts for these automata models. This is a joint work with Alin Bostan, Arnaud Carayol and Cyril Nicaud.
|Dernière modification : Monday 24 January 2022||Contact pour cette page : Cyril.Banderier at lipn.univ-paris13.fr|