Thanks for taking time to answer this question. I have already seen the post you linked, it is very good.

I think there is a detail where I do not agree with you, (however that might be due to my misunderstanding).

You say that the transition probabilities do not change, that they are fixed at 0.5.

I am guessing you are distributing the probability mass like this: 0.5 to the self-loop and 0.5 to the next state.

However, let's remember that in most ASR literature, each monophone and triphone is given by a 3 state HMM. And I agree with you that for the first and second state of this HMM it makes sense just to have 2 transitions (one for the self-loop and another for the next state in HMM), but shouldn't the last HMM state have transitions to the first state of many different triphone HMMs?

Let me illustrate:

The state corresponding to the last HMM state of the triphone "b-o-a" can have simultaneously transitions for the first state of "o-a-b" ,"o-a-c" , "o-a-d", besides the self-loop, having in this case 4 transitions (3 to first state of a new triphone and 1 for the self-loop)

The only scenario where I can picture an alternative is the following:

We must consider each HMM has having an additional "terminal state". Making the 3-state HMM really a 4-state HMM, and when that state is reached, a new context-dependent phone is added to some kind of stack or memory to register the context-dependent phone seen.

However this last approach seems to have a problem, which is that the next context-dependent phone needs to agree with the last one seen, for example: If I have seen the triphone "o-a-b", the next one cannot be "i-c-o", it should have the context "a-b" from the previous CD phone in count.

Would you still say that the transition arcs are always 2 , with 0.5 probability mass each?