Conjugacy and equivalence of weighted automata
This talk starts with a result witin classical Finite Automata Theory:
'Two regular languages with the same number of words for each length can be mapped one onto the other by a letter-to-letter (finite) transducer'.
The notion of generating function of regular languages leads to the
introduction of the model of weighted automata. The conjugacy of weighted automata, a concept borrowed to symbolic dynamics, is then defined and it is shown how the above statement can be derived from the central result of this work: 'Two equivalent weighted automata are conjugate to a third one when the weight semiring is B, N, Z, or any Euclidean domain (and thus any (skew) field)'.
The talk is based on a joint work with Marie-Pierre Béal and Sylvain
Lombardy.