Probabilistic finite-state machines are used today in a variety of areas in pattern recognition, or in fields to which pattern recognition is linked: computational linguistics, machine learning, time series analysis, circuit testing, computational biology, speech recognition and machine translation are some of them. In part I of this paper we survey these generative objects and study their definitions and properties. In part II, we will study the relation of probabilistic finite-state automata with other well known devices that generate strings as hidden Markov models and -grams, and provide theorems, algorithms and properties that represent a current state of the art of these objects.