# Learning Local Transductions Is Hard

DOI: 10.1007/s10849-004-2115-9

- Cite this article as:
- Jansche, M. J Logic Lang Inf (2004) 13: 439. doi:10.1007/s10849-004-2115-9

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## Abstract

Local deterministic string-to-string transductions arise in natural language processing (NLP) tasks such as letter-to-sound translation or pronunciation modeling. This class of transductions is a simple generalization of morphisms of free monoids; learning local transductions is essentially the same as inference of certain monoid morphisms. However, learning even a highly restricted class of morphisms, the so-called fine morphisms, leads to intractable problems: deciding whether a hypothesized fine morphism is consistent with observations is an NP-complete problem; and maximizing classification accuracy of the even smaller class of alphabetic substitution morphisms is APX-hard. These theoretical results provide some justification for using the kinds of heuristics that are commonly used for this learning task.