Abstract
Weighted finite-state automata pose a number of challenges for software developers. One particular difficulty is that ε-transitions must be treated more carefully than is necessary for unweighted automata. The usual weighted ε-closure algorithm always produces O(n 2) transitions for a ε-loop with n states. An approach that removes ε-loops without performing a full ε-closure is proposed and it is shown how this can be efficiently implemented using sparse matrix operations.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Backhouse, R.C., Carré, B.A.: Regular Algebra applied to path-finding problems. Journal of the Institute of Mathematics and its Applications 15, 161–186 (1975)
Beesley, K.R., Karttunen, L.: Finite State Morphology. CSLI Studies in Computational Linguistics. CSLI Publications, Stanford (2003), http://www.fsmbook.com
Berstel, J.: Transductions and context-free languages. BG Teubner, Stuttgart (1979)
George, A., Liu, J.W.: Computer solution of large sparse positive definite systems. Prentice-Hall, Englewood Cliff (1981)
Johnson, J.H.: INR - a program for computing finite state automata (unpublished manuscript, 1986)
Kempe, A., Baeijs, C., Gaál, T., Guingne, F., Nicart, F.: WFSC - a new weighted finite state compiler. In: H. Ibarra, O., Dang, Z. (eds.) CIAA 2003. LNCS, vol. 2759, pp. 108–120. Springer, Heidelberg (2003)
Kumar, S., Byrne, W.: A weighted finite state transducer implementation of the alignment template model for statistical machine translation. In: Proceedings of HLT-NAACL 2003, Edmonton, Canada, pp. 142–149 (2003)
Mohri, M.: Finite-state transducers in language and speech processing. Computational Linguistics 23(2), 269–312 (1997)
Mohri, M.: Generic ε-removal algorithm for weighted automata. In: Yu, S., Păun, A. (eds.) CIAA 2000. LNCS, vol. 2088, pp. 230–242. Springer, Heidelberg (2001)
Mohri, M.: Generic ε-removal and input ε-normalization algorithms for weighted transducers (2002)
Mohri, M., Pereira, F., Riley, M.: The design principles of a weighted finite-state transducer library. Theoretical Computer Science 231(1), 17–32 (2000)
Pereira, F., Riley, M.: Speech recognition by composition of weighted finite automata. In: Roche, E., Schabes, Y. (eds.) Finite-state Language Processing, pp. 431–453. The MIT Press, Cambridge (1997)
Rose, D.J., Tarjan, R.E.: Algorithmic aspects of vertex elimination. In: Proceedings of the 7th ACM Symposium on the Theory of Computing (STOC 1975), pp. 245–254 (1975)
Tarjan, R.E.: Fast algorithms for solving path problems. Journal of the ACM 28(3), 594–614 (1981)
van Noord, G.: Treatment of epsilon moves in subset construction. Computational Linguistics 26(1), 61–76 (2000)
van Noord, G., Gerdemann, D.: An extendible regular expression compiler for finite-state approaches in natural language processing. In: Boldt, O., Jürgensen, H. (eds.) WIA 1999. LNCS, vol. 2214, p. 122. Springer, Heidelberg (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Johnson, J.H. (2006). Collapsing ε-Loops in Weighted Finite-State Machines. In: Yli-Jyrä, A., Karttunen, L., Karhumäki, J. (eds) Finite-State Methods and Natural Language Processing. FSMNLP 2005. Lecture Notes in Computer Science(), vol 4002. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780885_12
Download citation
DOI: https://doi.org/10.1007/11780885_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35467-3
Online ISBN: 978-3-540-35469-7
eBook Packages: Computer ScienceComputer Science (R0)