Stochastic (or, indifferently, probabilistic) sequential machines have been recognized to be important mathematical models for several classes of information processing systems with memory, in which random disturbances cannot be neglected. As examples it suffices to mention the models of finite-state discrete channels for information transmission, sequential machines constructed from unreliable components, and adaptive learning systems. From a more abstract and less engineering-motivated angle, the stochastic sequential machine (SSM) represents the natural generalization of the deterministic one, on which a considerable body of knowledge exists. Not to be overlooked, finally, is the fact that the rich underlying structure promises elegant results and this undeniable aesthetic dimension certainly contributes an additional interest to this per se attractive topic.