I'm majoring in pure linguistics (not computational), and I don't have any basic knowledge regarding computational science or mathematics. But I happen to take the "Automatic Speech Recognition" course in my graduate school and struggling with it.
I have a question regarding getting the formula for a component of the forward algorithm.
$$ \alpha_t(j) = \sum_{i=1}^{N} P(q_{t-1} = i, q_t=j, o_1^{t-1}, o^t|\lambda) $$
When $q$ is a hidden state, $o$ is a given observation, and $\lambda$ contains transition probability, emission probability and the start/end state.
Is the Markov assumption (the current state is only dependent upon the one right before it) assumed here? I thought so, because it contains $q_{t-1}=i$ and not $q_{t-2}=k$ or $q_{t-3}=l$.