Semirings, automata, languages
Semirings, automata, languages
Digital images and formal languages
Handbook of formal languages, vol. 3
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
Finite-state transducers in language and speech processing
Computational Linguistics
Rational Kernels: Theory and Algorithms
The Journal of Machine Learning Research
General Algorithms for Testing the Ambiguity of Finite Automata
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
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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 T1, T2, and T3resulting in T, is O(|T|Qmin (d(T1) d(T3), d(T2)) + |T|E), where |·|Qdenotes the number of states, |·|Ethe 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.