Transitive Hall sets

We give the definition of Lazard and Hall sets in the context of transitive factorizations of free monoids. The equivalence of the two properties is proved. This allows to build new effective bases of free partially commutative Lie algebras. The commutation graphs for which such sets exist are completely characterized and we explicit, in this context, the classical PBW rewriting process

Direct and dual laws for automata with multiplicities

We present here theoretical results coming from the implementation of the package called AMULT (automata with multiplicities in several noncommutative variables). We show that classical formulas are ``almost every time'' optimal, characterize the dual laws preserving rationality and also relators that are compatible with these laws

(k, l)-Unambiguity and Quasi-Deterministic Structures: An Alternative for the Determinization

International audienc