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Probabilistic finite-state machines - Part I. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005. Vol. 27 (7), pp. 1013-1025.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 $n$-grams, and provide theorems, algorithms and properties that represent a current state of the art of these objects.