Weighted Finite State Transducer

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A Weighted Finite State Transducer is a finite state transducer with weighted transitions (weighted edges).



References

2015

  • (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Finite_state_transducer#Weighted_automata Retrieved:2015-1-16.
    • Finite State Transducers can be weighted, where each transition is labeled with a weight in addition to the input and output labels. A Weighted Finite State Transducer (WFST) over a set K can be defined similarly to an unweighted one as an 8-tuple T=(Q, Σ, Γ, I, F, E, λ, ρ), where:
      • Q, Σ, Γ, I, F are defined as above;
      • [math]\displaystyle{ E \subseteq Q \times (\Sigma\cup\{\epsilon\}) \times (\Gamma\cup\{\epsilon\}) \times Q \times K }[/math] (where ε is the empty string) is the finite set of transitions;
      • [math]\displaystyle{ \lambda: I \rightarrow K }[/math] maps initial states to weights;
      • [math]\displaystyle{ \rho: F \rightarrow K }[/math] maps final states to weights.
    • In order to make certain operations on WFSTs well-defined, it is convenient to require the set of weights to form a semiring. Two typical semirings used in practice are the log semiring and tropical semiring: unweighted automata may be regarded as having weights in the Boolean semiring.


2007

2002