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On Rational Stochastic Languages

Denis F., Esposito Y.

Fundamenta Informaticae

2008

Vol. 86, nr 1-2

41-77

The goal of the present paper is to provide a study of rational stochastic languages over a semiring KÎ{ Q, R, Q+, R+}. A rational stochastic language is a probability distribution over a free monoid ?*, which is rational over K, that is, which can be generated by a multiplicity automaton with parameters in K. We study the relations between the classes of rational stochastic languages SKrat(σ). We define the notion of residual language of a stochastic language and we use it to investigate properties of several subclasses of rational stochastic languages. Then, we study the representation of rational stochastic languages by means of multiplicity automata. Lastly, we show some connections between properties of rational stochastic languages and results obtained in the field of probabilistic grammatical inference.