Abstract
We introduce a new class of probabilistic automata: Probabilistic Residual Finite State Automata. We show that this class can be characterized by a simple intrinsic property of the stochastic languages they generate (the set of residual languages is finitely generated by residuals) and that it admits canonical minimal forms. We prove that there are more languages generated by PRFA than by Probabilistic Deterministic Finite Automata (PDFA). We present a first inference algorithm using this representation and we show that stochastic languages represented by PRFA can be identified from a characteristic sample if words are provided with their probabilities of appearance in the target language.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
D. Angluin. Identifying languages from stochastic examples. Technical Report YALEU/DCS/RR-614, Yale University, New Haven, CT, 1988.
R.C. Carrasco and J. Oncina. Learning stochastic regular grammars by means of a state merging method. In International Conference on Grammatical Inference, pages 139–152, Heidelberg, September 1994. Springer-Verlag.
R. C. Carrasco and J. Oncina. Learning deterministic regular grammars from stochastic samples in polynomial time. RAIRO (Theoretical Informatics and Applications), 33(1):1–20, 1999.
F. Denis, A. Lemay, and A. Terlutte. Learning regular languages using non deterministic finite automata. In ICGI’2000, 5th International Colloquium on Grammatical Inference, volume 1891 of Lecture Notes in Artificial Intelligence, pages 39–50. Springer Verlag, 2000.
F. Denis, A. Lemay, and A. Terlutte. Learning regular languages using rfsa. In ALT 2001. Springer Verlag, 2001.
F. Denis, A. Lemay, and A. Terlutte. Residual finite state automata. In 18th Annual Symposium on Theoretical Aspects of Computer Science, volume 2010 of Lecture Notes in Computer Science, pages 144–157, 2001.
K. J. Lang, B. A. Pearlmutter, and R. A. Price. Results of the Abbadingo one DFA learning competition and a new evidence-driven state merging algorithm. In Proc. 4th International Colloquium on Grammatical Inference-ICGI 98, volume 1433 of Lecture Notes in Artificial Intelligence, pages 1–12. Springer-Verlag, 1998.
J. Oncina and P. Garcia. Inferring regular languages in polynomial update time. In Pattern Recognition and Image Analysis, pages 49–61, 1992.
A. Stolcke and S. Omohundro. Inducing probabilistic grammars by Bayesian model merging. Lecture Notes in Computer Science, 862:106–118, 1994.
Franck Thollard, Pierre Dupont, and Colin de la Higuera. Probabilistic DFA inference using Kullback-Leibler divergence and minimality. In Proc. 17th International Conf. on Machine Learning, pages 975–982. Morgan Kaufmann, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Esposito, Y., Lemay, A., Denis, F., Dupont, P. (2002). Learning Probabilistic Residual Finite State Automata. In: Adriaans, P., Fernau, H., van Zaanen, M. (eds) Grammatical Inference: Algorithms and Applications. ICGI 2002. Lecture Notes in Computer Science(), vol 2484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45790-9_7
Download citation
DOI: https://doi.org/10.1007/3-540-45790-9_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44239-4
Online ISBN: 978-3-540-45790-9
eBook Packages: Springer Book Archive