3.1.2. Lexicon model p Sð Þ jW

p Sð Þ jW can be further factorized using a probabilistic chain rule and Markov assumption (first order) as follows:

$$p(\mathcal{S}|\mathcal{W}) = \prod\_{t=1}^{T} p(\mathbf{s}\_t|\mathbf{s}\_1, \dots, \mathbf{s}\_{t-1}, \mathcal{W}) \tag{10}$$

$$\varepsilon \approx \prod\_{t=1}^{T} p(\mathbf{s}\_t | \mathbf{s}\_{t-1}, \mathcal{W}) \tag{11}$$

An HMM state transition represents this probability. A pronunciation dictionary performs the conversion from w to HMM states through phoneme representation.
