Sylvain Lombardy

Conjugacy and equivalence of weighted automata and functional transducers

We show that two equivalent

Deciding unambiguity and sequentiality from a finitely ambiguous max-plus automaton

\mathbb{K}

Introducing VAUCANSON

-automata are conjugate to a third one, when

On the equivalence of Z -automata

\mathbb{K}

ON THE FINITENESS PROBLEM FOR AUTOMATON (SEMI)GROUPS

is equal to

Deciding Unambiguity and Sequentiality of Polynomially Ambiguous Min-Plus Automata

\mathbb{B, N, Z}

Series which are both max-plus and min-plus rational are unambiguous

, or any (skew) field and that the same holds true for functional tranducers as well.

Inside vaucanson

Finite automata with weights in the max-plus semiring are considered. The main result is: it is decidable whether a series that is recognized by a finitely ambiguous max-plus automaton is unambiguous, or is sequential. Furthermore, the proof is constructive. A collection of examples is given to illustrate the hierarchy of max-plus series with respect to ambiguity.

THE VALIDITY OF WEIGHTED AUTOMATA

This paper reports on a new software platform called VAUCANSON and dedicated to the computation with automata and transducers. Its main feature is the capacity of dealing with automata whose labels may belong to various algebraic structures.The paper successively describes the main features of the VAUCANSON platform, including the fact that the very rich data structure used to implement automata does not weigh too much on the performance, shows how VAUCANSON allows to program algorithms on automata in a way which is very close to the mathematical expression of the algorithm and finally explains the main choices of the programming design that enable to achieve both genericity and efficiency.

How Expressions Can Code for Automata

We prove that two automata with multiplicity in