We present a learning algorithm for local phonological processes that relies on a restriction on the expressive power needed to compute phonological patterns that apply locally. Representing phonological processes as a functional mapping from an input to output form (an assumption compatible with either the SPE or OT formalism), the learner assumes the target process can be described with the functional counterpart to the Strictly Local (McNaughton and Papert 1971, Rogers and Pullum 2011) formal languages. Given a data set of input-output string pairs, the learner applies the two-stage grammatical induction procedure of 1) constructing a prefix tree representation of the input and 2) generalizing the pattern to words not found in the data set by merging states (Garcia and Vidal 1990, Oncina et al. 1993, Heinz 2007, 2009, de la Higuera 2010). The learner’s criterion for state merging enforces a locality requirement on the kind of function it can converge to and thereby directly reflects its own hypothesis space. We demonstrate with the example of German final devoicing, using a corpus of string pairs derived from the CELEX2 lemma corpus. The implications of our results include a proposal for how humans generalize to learn phonological patterns and a consequent explanation for why local phonological patterns have this property.