The Tier-based Strictly 2-Local (TSL2) languages are a class of formal languages which have been shown to model long-distance phonotactic generalizations in natural language (Heinz et al., 2011). This paper introduces the Tier-based Strictly 2-Local Inference Algorithm (2TSLIA), the first nonenumerative learner for the TSL2 languages. We prove the 2TSLIA is guaranteed to converge in polynomial time on a data sample whose size is bounded by a constant.

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