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We describe PyFoma, an open-source Python module for constructing weighted and unweighted finite-state transducers and automata from regular expressions, string rewriting rules, right-linear grammars, or low-level state/transition manipulation. A large variety of standard algorithms for working with finite-state machines is included, with a particular focus on the needs of linguistic and NLP applications. The data structures and code in the module are designed for legibility to allow for potential use in teaching the theory and algorithms associated with finite-state machines.