The following gives the encoding of all n-gram models produced by the utilities here, including those with unnormalized counts, as a cyclic weighted finite-state transducer in OpenFst format.

An n-gram is a sequence of *k* symbols: *w _{1} ... w_{k}*. Let

- There is a
*unigram*state in every model, representing the empty string. - Every proper prefix of every n-gram in
*N*has an associated state in the model. - The state associated with an n-gram
*w*has a backoff transition (labeled with_{1}... w_{k}*⟨epsilon⟩*) to the state associated with its suffix*w*._{2}... w_{k} - An n-gram
*w*is represented as a transition, labeled with_{1}... w_{k}*w*, from the state associated with its prefix_{k}*w*to a destination state defined as follows:_{1}... w_{k-1}- If
*w*is a proper prefix of an n-gram in the model, then the destination of the transition is the state associated with_{1}... w_{k}*w*_{1}... w_{k} - Otherwise, the destination of the transition is the state associated with the suffix
*w*._{2}... w_{k}

- If
- Start and end of the sequence are not represented via transitions in the automaton or symbols in the symbol table. Rather
- The start state of the automaton encodes the "start of sequence" n-gram prefix (commonly denoted
*⟨s⟩*). - The end of the sequence (often denoted
*⟨/s⟩*) is included in the model through state final weights, i.e., for a state associated with an n-gram prefix*w*, the final weight of that state represents the weight of the n-gram_{1}... w_{k}*w*._{1}... w_{k}⟨/s⟩

- The start state of the automaton encodes the "start of sequence" n-gram prefix (commonly denoted

-- MichaelRiley - 09 Dec 2011

Topic revision: r1 - 2011-12-09 - MichaelRiley

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