Viterbi Algorithm Generalized for n-Tape Best-Path Search

Details Viterbi Algorithm Generalized for n-Tape Best-Path Search Viterbi Algorithm Generalized for n-Tape Best-Path Search

2006-12-07

arxiv.org/abs/cs/0612041v1

Proc. FSMNLP 2009, Pretoria, South Africa. July 21-24. (improved version).

Computer Science

Computation and Language

12 pages, 3 figures, LaTeX (+ .eps)

Scientific paper

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.

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