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# Learning Input Strictly Local Functions From Their Composition

*Proceedings of the Fifteenth International Conference on Grammatical Inference*, PMLR 153:47-65, 2021.

#### Abstract

This paper studies the learning of two functions given positive samples of their composition, motivated by an empirical problem in natural language phonology. Empirically relevant conditions under which this is possible are identified and a provably correct algorithm is given that can

*semi-strongly*identify the two functions in polynomial time and data. In order to clearly illustrate the learning problem and related concepts, we focus on a simple subset of*input strictly 2-local functions*. But we further argue that the general learning procedure we propose can be extended to more general classes of functions.