3-Way composition of weighted finite-state transducers

Cyril Allauzen, Mehryar Mohri

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationImplementation and Application of Automata - 13th International Conference, CIAA 2008, Proceedings
Number of pages12
StatePublished - 2008
Event13th International Conference on Implementation and Application of Automata, CIAA 2008 - San Francisco, CA, United States
Duration: Jul 21 2008Jul 24 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5148 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other13th International Conference on Implementation and Application of Automata, CIAA 2008
Country/TerritoryUnited States
CitySan Francisco, CA

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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