Some relations among stochastic finite state networks used in automatic speech recognition

In the literature on automatic speech recognition, the popular hidden Markov models (HMMs), left-to-right hidden Markov models (LRHMMs), Markov source models (MSMs), and stochastic regular grammars (SRGs) are often proposed as equivalent models. However, no formal relations seem to have been established among these models to date. A study of these relations within the framework of formal language theory is presented. The main conclusion is that not all of these models are equivalent, except certain types of hidden Markov models with observation probability distribution in the transitions, and stochastic regular grammar