Viterbi Algorithm Generalized for n-Tape Best-Path Search
<|reference_start|>Viterbi Algorithm Generalized for n-Tape Best-Path Search: We present a generalization of the Viterbi algorithm for identifying the path with minimal (resp. maximal) weight in a n-tape weighted finite-state machine (n-WFSM), that accepts a given n-tuple of input strings (s_1,... s_n). It also allows us to compile the best transduction of a given input n-tuple by a weighted (n+m)-WFSM (transducer) with n input and m output tapes. Our algorithm has a worst-case time complexity of O(|s|^n |E| log (|s|^n |Q|)), where n and |s| are the number and average length of the strings in the n-tuple, and |Q| and |E| the number of states and transitions in the n-WFSM, respectively. A straight forward alternative, consisting in intersection followed by classical shortest-distance search, operates in O(|s|^n (|E|+|Q|) log (|s|^n |Q|)) time.<|reference_end|>
@article{kempe2006viterbi,
    title={Viterbi Algorithm Generalized for n-Tape Best-Path Search},
    author={Andr'e Kempe},
    journal={Proc. FSMNLP 2009, Pretoria, South Africa. July 21-24. (improved
  version).},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0612041},
    primaryClass={cs.CL cs.DS cs.SC}
}