ABSTRACT
One of the motivating forces behind the mathematical development of hidden Markov models 1 has been the need of statisticians, engineers, and computer scientists for time-series models that are at the same time sufficiently simple for practical computation and sufficiently complex to allow effective modeling of highly nonstationary processes. The list of such processes includes sampled versions of continuous processes, such as the speech signal, the various signals arising in image processing, signals associated with handwriting, and the like. The list also includes inherently discrete processes, such as those arising in the textual (as opposed to acoustic) study of language, statistical language translation, and coding. Another force behind this development was the emergence of the finite-state machine as a basic tool of computer science.
