A Hidden Markov Model is given by transition and emission matrices. The transition matrix determine probability of "next states" as a function of the current state. The emission matrix determine the probability of observations as a function of the current state.
In this formulation we assume that "transitions" and "emissions" are independent. But what if they are not? In other words, what if the probability of a particular observation (given the current state) and probability of a particular transitions are bound?
Can such a model be somehow transformed into a classical HMM (with a transition and emission matrices)? And, if not, how to approach such problem? For example, is there some replacement of the Viterbi and Baum-Welch algorithms for such an "extended" HMM?