Rational stochastic languages
<|reference_start|>Rational stochastic languages: The goal of the present paper is to provide a systematic and comprehensive study of rational stochastic languages over a semiring K \in {Q, Q +, R, R+}. A rational stochastic language is a probability distribution over a free monoid \Sigma^* which is rational over K, that is which can be generated by a multiplicity automata with parameters in K. We study the relations between the classes of rational stochastic languages S rat K (\Sigma). We define the notion of residual of a stochastic language and we use it to investigate properties of several subclasses of rational stochastic languages. Lastly, we study the representation of rational stochastic languages by means of multiplicity automata.<|reference_end|>
@article{denis2006rational,
    title={Rational stochastic languages},
    author={Franc{c}ois Denis (LIF), Yann Esposito (LIF)},
    journal={arXiv preprint arXiv:cs/0602093},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0602093},
    primaryClass={cs.LG cs.CL}
}