Abstract
Composition of weighted transducers is a fundamental algorithm used in many applications, including for computing complex edit-distances between automata, or string kernels in machine learning, or to combine different components of a speech recognition, speech synthesis, or information extraction system. We present a generalization of the composition of weighted transducers, 3-way composition, which is dramatically faster in practice than the standard composition algorithm when combining more than two transducers. The worst-case complexity of our algorithm for composing three transducers T 1, T 2, and T 3 resulting in T, is O(|T| Q min (d(T 1) d(T 3), d(T 2)) + |T| E ), where |·| Q denotes the number of states, |·| E the number of transitions, and d(·) the maximum out-degree. As in regular composition, the use of perfect hashing requires a pre-processing step with linear-time expected complexity in the size of the input transducers. In many cases, this approach significantly improves on the complexity of standard composition. Our algorithm also leads to a dramatically faster composition in practice. Furthermore, standard composition can be obtained as a special case of our algorithm. We report the results of several experiments demonstrating this improvement. These theoretical and empirical improvements significantly enhance performance in the applications already mentioned.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Berstel, J.: Transductions and Context-Free Languages. Teubner (1979)
Chen, S., Goodman, J.: An empirical study of smoothing techniques for language modeling. Technical Report, TR-10-98, Harvard University (1998)
Cortes, C., Haffner, P., Mohri, M.: Rational Kernels: Theory and Algorithms. Journal of Machine Learning Research 5, 1035–1062 (2004)
Culik II, K., Kari, J.: Digital Images and Formal Languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, pp. 599–616. Springer, Heidelberg (1997)
Eilenberg, S.: Automata, Languages and Machines. Academic Press, London (1974–1976)
Katz, S.M.: Estimation of probabilities from sparse data for the language model component of a speech recogniser. IEEE Transactions on Acoustic, Speech, and Signal Processing 35(3), 400–401 (1987)
Kuich, W., Salomaa, A.: Semirings, Automata, Languages. Springer, Heidelberg (1986)
Mohri, M.: Finite-State Transducers in Language and Speech Processing. Computational Linguistics 23(2) (1997)
Mohri, M.: Edit-Distance of Weighted Automata: General Definitions and Algorithms. Int. J. Found. Comput. Sci. 14(6), 957–982 (2003)
Mohri, M.: Statistical Natural Language Processing. In: Lothaire, M. (ed.) Applied Combinatorics on Words. Cambridge University Press, Cambridge (2005)
Mohri, M., Pereira, F.C.N., Riley, M.: Weighted Automata in Text and Speech Processing. In: Proceedings of the 12th biennial European Conference on Artificial Intelligence (ECAI 1996). John Wiley and Sons, Chichester (1996)
Pereira, F., Riley, M.: Finite State Language Processing. In: Speech Recognition by Composition of Weighted Finite Automata. The MIT Press, Cambridge (1997)
Perrin, D.: Words. In: Lothaire, M. (ed.) Combinatorics on words, Cambridge Mathematical Library. Cambridge University Press, Cambridge (1997)
Salomaa, A., Soittola, M.: Automata-Theoretic Aspects of Formal Power Series. Springer, Heidelberg (1978)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Allauzen, C., Mohri, M. (2008). 3-Way Composition of Weighted Finite-State Transducers. In: Ibarra, O.H., Ravikumar, B. (eds) Implementation and Applications of Automata. CIAA 2008. Lecture Notes in Computer Science, vol 5148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70844-5_27
Download citation
DOI: https://doi.org/10.1007/978-3-540-70844-5_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70843-8
Online ISBN: 978-3-540-70844-5
eBook Packages: Computer ScienceComputer Science (R0)