1 Introduction
First order Hidden Markov Models (HMM) are the most commonly used stochastic models in speech recognition. They are defined with a set of imposed conditional independence assumptions. Indeed, the observations are assumed to be governed by a hidden (unobserved) dynamic process. The associated independence assumptions state that the hidden process is first-order Markov, and each observation depends only on the current hidden variable. There is, however, a fundamental question regarding these dependency assumptions: are they realistic hypothesis for any kind of speech recognition task?