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This paper proposes to model the extraction of acronyms and their meaning from unstructured text as a stochastic process using hidden Markov models (HMMs). The underlying, or hidden, chain is derived from the acronym, where the states in the chain are made by the acronyms characters. The transition between two states happens when the origin state emits a signal. Signals recognizable by the HMM are the tokens extracted from text. Observations are the sequence of tokens also extracted from text. Given a set of observations, the acronym definition will be the observation with the highest probability to emerge from the HMM. Modeling this extraction probabilistically allows us to deal with two difficult aspects of this process: ambiguity and noise. We characterize ambiguity when there is no unique alignment between the characters in the acronym with a token in the expansion, while the feature-characterizing noise is the absence of such alignment. Our experiments have proven that this approach has high precision (93.50%) and recall (85.50%) rates in an environment, where acronym coinage is ambiguous and noisy, such as the biomedical domain. Processing and comparing the approached described in this paper with different others showed that the former reaches the highest F1 score (89.40%) on the same corpus.