  Given a finite set of words w1,...,wn independently drawn according to a
fixed unknown distribution law P called a stochastic language, an usual goal in
Grammatical Inference is to infer an estimate of P in some class of
probabilistic models, such as Probabilistic Automata (PA). Here, we study the
class of rational stochastic languages, which consists in stochastic languages
that can be generated by Multiplicity Automata (MA) and which strictly includes
the class of stochastic languages generated by PA. Rational stochastic
languages have minimal normal representation which may be very concise, and
whose parameters can be efficiently estimated from stochastic samples. We
design an efficient inference algorithm DEES which aims at building a minimal
normal representation of the target. Despite the fact that no recursively
enumerable class of MA computes exactly the set of rational stochastic
languages over Q, we show that DEES strongly identifies tis set in the limit.
We study the intermediary MA output by DEES and show that they compute rational
series which converge absolutely to one and which can be used to provide
stochastic languages which closely estimate the target.
