Abstract
We present a new generic ε-removal algorithm for weighted automata and transducers defined over a semiring. The algorithm can be used with any semiring covered by our framework and works with any queue discipline adopted. It can be used in particular in the case of unweighted automata and transducers and weighted automata and transducers defined over the tropical semiring. It is based on a general shortest-distance algorithm that we briefly describe. We give a full description of the algorithm including its pseudocode and its running time complexity, discuss the more efficient case of acyclic automata, an on-the-fly implementation of the algorithm and an approximation algorithm in the case of the semirings not covered by our framework. We also illustrate the use of the algorithm with several semirings.
This is a preview of subscription content, log in via an institution to check access.
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
A.V. Aho, R. Sethi, and J.D. Ullman. Compilers, Principles, Techniques and Tools. Addison Wesley: Reading, MA, 1986.
K. Culik II and J. Kari. Digital images and formal languages. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, pages 599–616. Springer, 1997.
R.W. Floyd. Algorithm 97 (shortest path). Communications of the ACM, 18, 1968.
M.L. Fredman and R.E. Tarjan. Fibonacci heaps and their uses in improved optimalization problems. Communications of the ACM, 34, 1987.
W. Kuich and A. Salomaa. Semirings, Automata, Languages. Number 5 in EATCS Monographs on Theoretical Computer Science. Springer-Verlag, Berlin-New York, 1986.
M. Mohri. Finite-State Transducers in Language and Speech Processing. Computational Linguistics, 23:2, 1997.
M. Mohri. General Algebraic Frameworks and Algorithms for Shortest-Distance Problems. Technical Memorandum 981210-10TM, AT&T Labs-Research, 62 pages, 1998.
M. Mohri, F.C.N. Pereira, and M. Riley. The design principles of a weighted finite-state transducer library. Theoretical Computer Science, 231:17–32, January 2000.
K. Thompson. Regular expression search algorithm. Comm. ACM, 11, 1968.
G. van Noord. Treatment of epsilon moves in subset construction. Computational Linguistics, 26:1, 2000.
S. Warshall. A theorem on boolean matrices. Journal of the ACM, 9(1):11–12, 1962.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mohri, M. (2001). Generic ε-Removal Algorithm for Weighted Automata. In: Yu, S., Păun, A. (eds) Implementation and Application of Automata. CIAA 2000. Lecture Notes in Computer Science, vol 2088. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44674-5_19
Download citation
DOI: https://doi.org/10.1007/3-540-44674-5_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42491-8
Online ISBN: 978-3-540-44674-3
eBook Packages: Springer Book Archive