>
> I found the following slide describing the relationship between HMM
> and WFST:


That is not a good way of integrating HMMs and WFSTs.

Please see the original literature on WFSTs and speech recognition for how
to do this.  The following paper, for example, describes the combination of
Gaussian mixture models with WFSTs:

Weighted finite-state transducers in speech
recognition<http://www.isca-speech.org/archive/asr2000/asr0_097.html>-
►*nyu.edu <http://www.cs.nyu.edu/%7Emohri/postscript/csl01.pdf> [PDF] *
M Mohri, F Pereira, M Riley - ASR2000-Automatic Speech Recognition:
Challenges for the new …, 2000 - ISCA

Tom

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