Given a set of phonological features, we can enumerate a set of phonological classes. Here we consider the inverse of this problem: given a set of phonological classes, can we derive a feature system? We show that this is indeed possible, using a collection of algorithms that assign features to a set of input classes and differ in terms of what types of features are permissible. This work bears on theories of both language-specific and universal features, provides testable predictions of the featurizations available to learners, and serves as a useful component in computational models of feature learning.

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