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On Rational Stochastic Languages

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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.
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41--77
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bibliogr. 26 poz., wykr.
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Bibliografia
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  • [7] Dempster, A., Laird, N. M., Rubin, D. B.: Maximum likelihood from incomplete data via the EMalgorithm., Journal of the Royal Statistical Society, 39, 1977, 1-38.
  • [8] Denis, F., Esposito, Y.: Residual languages and probabilistic automata, 30th International Colloquium, ICALP 2003, number 2719 in LNCS, SV, 2003.
  • [9] Denis, F., Esposito, Y.: Learning classes of Probabilistic Automata, COLT 2004, number 3120 in LNAI, 2004.
  • [10] Denis, F., Esposito, Y., Habrard, A.: Learning Rational stochastic languages, Proc. of the 19th Annual Conference on Learning Theory, 4005, 2006.
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  • [13] Denis, F., Lemay, A., Terlutte, A.: Learning Regular languages using RFSAs, Theoretical Computer Science, 2(313), 2004, 267-294.
  • [14] Dupont, P., Denis, F., Esposito, Y.: Links between Probabilistic Automata and Hidden Markov Models: probability distributions, learning models and induction algorithms, Pattern Recognition: Special Issue on Grammatical Inference Techniques & Applications, 38/9, 2005, 1349-1371.
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  • [19] Habrard, A., Denis, F., Esposito, Y.: Using Pseudo-stochastic Rational Languages in Probabilistic Grammatical Inference, ICGI (Y. Sakakibara, S. Kobayashi, K. Sato, T. Nishino, E. Tomita, Eds.), 4201, Springer, 2006, ISBN 3-540-45264-8.
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Bibliografia
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bwmeta1.element.baztech-article-BUS5-0018-0003
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